To go back to the original question posed, whether or not a Church has apostolic succession is crucial to the question of whether its presbyters and hierarchs have valid orders and, accordingly, whether the Holy Mysteries administered to its faithful by those presbyters are valid. Working backward, from the question of validity of orders and the faculty, authority, and jurisdiction inherent therein, the Orthodox stance - were an official one to be offered - would most likely be in the negative.
In the past 2 days, I have posted on nearly identical topics in 3 different threads on two other fora. Since my explanation yielded a compliment from a ROCOR cleric who is much more conservative in his thinking than me, but whose opinion I value, I'll offer a slightly modified version of it here, in hopes of giving some answer to Denny's original query.
"The theological praxis of Catholics and Orthodox as to the validity of orders and the dependent issue of the validity of sacraments differs significantly.
There are basically two theories of apostolic succession and, in most instances, the application of the theory held by a given Church effectively determines the validity accorded to claimed presbyteral and episcopal orders and, ipso facto, the validity of sacraments administered by those claiming to possess valid orders, whether presbyteral and/or episcopal (putting aside issues as to form and intent, since if there is no validity to the orders of the sacrament's minister, other considerations are of no consequence to either Church).
If the orders claimed to be possessed are themselves invalid, the sacraments derived from him who claims to possess orders will, in turn, be invalid if the sacrament is one which requires administration by an ordained minister - essentially any except baptism in extremis in both the Catholic and Orthodox Churches and marriage in the Latin Church, where the cleric is seen as witness to the Sacrament and the couple as the ministers, as opposed to the Eastern and Oriental Catholic and Orthodox Churches where the cleric is the actual minister.
The Augustinian theory effectively holds that valid episcopal ordination confers an indelible character that is not affected by any schismatic or heretical act or excommunication taken in response thereto or for any other reason. Accordingly, a validly ordained priest once validly ordained to the episcopate retains his capacity to exercise that order, though he may have been deprived juridically of the office or jurisdiction by which he performed episcopal acts. The latter considerations affect only the licitness of his acts.
The Cyprianic theory effectively holds that a valid episcopal ordination is affected by subsequent schismatic or heretical acts and by excommunication taken in response thereto or for any other reason. Accordingly, a validly ordained priest once validly ordained to the episcopate retains his capacity to exercise that order only so long as he continues in communion with the jurisdiction under the authority of which he was ordained to the episcopate (or such other jurisdiction into which he may have subsequently been accepted) and is exercising the office or jurisdiction by which he has the right to perform those acts. There is no distinction made as to licitness.
The Catholic Church adheres to the Augustinian theory; the Orthodox Churches to the Cyprianic theory, (although they have elected to exercise oekonomia in application of it to instances in which schismatic bodies have returned to communion).
Frankly, the Augustinian theory has been or certainly has become a thorn in the side of the Catholic Church. It effectively assures that all manner of independent hierarchs, both those who pursue their perceived vocation with spiritual and intellectual honesty and those who are episcopi vagante in the most perjorative connotation accorded to the phrase, can sleep at night with at least a modicum of assurance that they possess valid episcopal orders, unless form or intent are at issue. The time-honored practice in the so-called "independent" Catholic and Orthodox movements of garnering multiple episcopal consecrations or, subsequently, being re-consecrated sub conditione is effectively a means of leveraging the Augustinian theory. Most such hierarchs operate on the premise that "more is better" or "there has to be at least one good one here somewhere". With most having an episcopal genealogy that traces back through an average of 30 ancestral lines of succession, from a combination of dissident Latin Catholic, Eastern and Oriental Catholic, Eastern and Oriental Orthodox hierarchs, they can feel reasonably secure. Those lines which cannot be proven valid because there is serious doubt as to the validity of one actor (e.g., the so-called Melkite-Aneed Line) can and do feel comfortably buffered by Duarte and Thuc Lines.
People sometimes point to subsequent acts by bishops of these "Churches" which break faith with Catholic doctrine and erroneously perceive these as breaking the line of apostolic succession. For instance, no bishop, regardless of the validity of his episcopal orders, can validly ordain a woman. But, that he did so would not invalidate his subsequent ordination of a man, with proper intent and according to proper form. So, it is possible to go rather far afield theologically yet still retain apostolic succession.
The Orthodox Churches, relying on the canonically legal status of the hierarch conferring orders (his status in communion with a recognized jurisdiction to which the Church accords canonical status), have a much simpler task before them in assessing validity and, since they do not make the distinction of licitness, the end result is clear-cut.
Given its historical ties to the Cyprianic theory, it stands to reason that the Orthodox would not accord validity to Catholic orders or sacraments and that any do so must be seen as an exercise of charity on their part, applying a measure of recognition to the common historical origins of Catholicity and Orthodoxy. We, as Catholics, can dislike the fact that all do not choose to do so, but it is not our place to impose upon others our theological precepts and require that they adopt them.
The potentially most ironic consideration here is that, applying the Augustinian theory, the Catholic Church would in some instances likely accept the validity of presbyteral and episcopal orders, and, consequently, sacraments, of "independent Orthodox" (and by that I do not mean those essentially mainstream Orthodox Churches which are typically termed "non-canonical" or "of iregular status", but those of the so-called "independent movement") whom the Orthodox themselves would, rightfully, never deem to be of their Communion, under even the most liberal of interpretations."
That said, as someone already noted, the Catholic Church has generally dismissed the validity of apostolic succession by the Anglican Churches on the basis of lapses in succession and, where such wasn't shown, by defects of form and/or intent. In recent times, some Anglican orders have been accepted by Rome as valid on the basis that validity of episcopal orders was supplied through interaction with Old Catholic hierarchs and hierarchs of some of those "independent Orthodox" hierarchs about whom I spoke above. It should be clear, however, that application of the Cyprianic theory would preclude Orthodox recognition of Anglican orders without ever reaching the question of lapses in the episcopal genealogical line (since communion didn't exist with a canonically recognized jurisdiction), let alone issues of form or intent.