For what my ten cents is worth:
The short answer to "could it happen to the Orthodox" is this: It would be a particularly foolish priest or bishop who would even try. If he did, he would be called before his superior, pronto, and asked to explain himself. Chances are, even if the infraction was relatively minor, he may well have to serve out a period of penance (such as withdrawal of the right to hear confessions).
If anything as "innovative" or grotesque as a "puppet liturgy" was ever to take place in an Orthodox church, I would bet anything that the gathered laity would rise up and prevail upon the errant priest right there and then to cease and desist. If he's lucky, he might not even be frogmarched out of the church by the yiayies or the babushki!
To be fair to our RC friends on this forum, not all of the RC world is as loopy as some of those in the US. Standards are being maintained in at least some
parts of the world. A parallel would be the case in late 2004 of a Roman Catholic priest in the Australian city of Brisbane who, of his own volition, performed a number of baptisms in the name of "the Creator, Liberator and Sustainer", instead of "the Father, Son and Holy Spirit". Not surprisingly, the Archbishop of Brisbane ordered the errant priest to stop this practice immediately.
The highest-ranking Roman Catholic cleric in Australia, the Archbishop of Sydney, Cardinal George Pell, also entered the fray, as was his responsibility. He ensured an investigation was instituted to determine the sacramental validity or otherwise of these baptisms. The Vatican has now decreed that this unconventional wording renders such baptisms invalid, as it is not according to the canonical Trinitarian "formula", therefore people thus baptised must be baptised again to restore sacramental validity.
The scary thing is that the errant priest had conducted such baptisms for something like ten years, and was only brought to account when the grandfather of a child to be baptised heard the wording, and approached his local bishop with his concerns.