I don't doubt it. The only part of Roman Catholicism that seems to be moderately thriving is the traditional sector. Even seminaries that require 7 years of training, like Our Lady of Guadalupe Seminary run by the traditionalist FSSP, have higher output than their Novus Ordo counterparts.
I apologize, but this issue is a pet peeve of mine so I'm going to rant about it for a bit.
First, it is true that Our Lady of Guadalupe Seminary is over-applied and has to turn down applicants. They have also recently greatly increased their facility, IIRC they expanded from being able to take 50 seminarians per year to 150. (note that this is for a 7 year program, so that means that at the previous size a maximum of 7 per year would become priests, assuming no one fell out of the program). That is not really surprising, looking at it sociologically, since traditionalism of various forms is a nation-wide movement (with many congregations, a high birth rate and a highly strong socialization rate which would foster a number of vocations. And the FSSP is to my knowledge the only seminary-type program that would cater to that market). Nevertheless, since the FSSP is not schismatic a Catholic would have to rejoice at this, and indeed the 3-4 FSSP seminarians I met seemed to be the types who would make great priests.
That being said, the size of "regular" diocesan structures in my experience dwarfs the weight of the traditionalist movement. To talk priestly vocations, one diocese I've been to has 30-some people in the seminary right now, and has I believe 7 join up this year (I've met 3-4 of these dudes). Another diocese had something around 1000 people become Catholic this past Holy Saturday through the RCIA program - a number greater than the entire traditionalist presence in that diocese and its two neighbors. (we also hope that since they went through the RCIA process, most came out of conviction instead of "I'll do this to make my spouse's parents happy", who have alternate mechanisms).
So the traditionalist movement is thriving, but I think the regular Catholic system is also thriving in certain areas, and regardless it dwarfs traditionalism simply due to size.
As to the title of this thread.....
.... it depends of course on what one means by "liberal". If one bases simply on what political issues they preach about, there are a good number of politically liberal (i.e. preach about issues in a way that shows they prefer the Democrats) Catholic priests, perhaps a third or so of the ones I happen to know, in my area.
If one means "liberal" in the sense of what's been called in academia "liberal" theology for the past 150 years or so (the sorts of things you see in most mainline protestant churches), about 25% of the Catholic priests I've met in my area essentially fit that description (with the highest proportion in the Jesuits), while I've never met an Orthodox priest who espouses that kind of theology. At the same time, I've never met a Catholic priest under the age of 50 (which accounts for about 50% of the priests I know) who is for "liberal" theology. Most/all of these folks seem adhere very strongly to the present Catechism/papal line.
