If I may, I’ll add a couple of thoughts to what has already been said:
Now, as to your question…
It’s possible.
Depending on where you live, though, the likelihood of such a possibility varies.
In my nation, for instance - the United States - such a scenario is almost certainly not going to happen. Too much politics/controversy/etc. regarding clerical celibacy as a mandatory discipline.
It also depends on which autonomous Eastern Catholic Church you’re joining. Let’s stick with the United States as an example. Maybe it could happen if you’re subject to, say, the Melkite Catholic bishop of Newton. But I’m almost positive a former Latin is not going to be ordained a priest in, say, the Byzantine Catholic Metropolitan Church of Pittsburgh (Ruthenian Catholic).
Other factors to consider are age, as well as longevity within the Church to which one has transferred.
Typically, married men are ordained later in life (over age 35) and, again typically, would have been married for some years before diaconal ordination. The basic idea is that a man has to be deemed stable in his state of life before ordination.
Now, if a person transfers Churches, those guidelines apply along with another: the person will have had to spend some years as a member of the Church in which he desires to be ordained.
For example, someone who transfers Churches at age 19, marries at age 21,and applies for consideration to seminary at age 22 is going to be rejected out of hand. The same would hold even if the transfer were done at age 35, marriage at 37, and application a year later. The one who transferred at age 19 might be accepted by age 35, while the one who transferred at age 35 might have a 10-15 year wait.
Let’s change the scenarios a bit. Say the 19 year old transfers Churches and then decides to apply for ordination. He will still have to wait some years before consideration is given. But let’s say he is accepted, and then marries while in seminary, say at age 30. His diaconal ordination will be delayed a while, and more than likely, priestly ordination would be delayed even longer. Most probably he would not achieve priestly ordination until he’s over 40. The one who transferred at age 35 would likely not achieve ordination for another 20 years.
And of course, lest I forget, the formal agreement of the wife is always required. Without that, there will be no ordination, diaconal or priestly, period.
I confess I find it unlikely in light of the fact that the Ruthenian Catholic Church’s bishops are appointed by the pope, and I don’t think Eastern Catholics are paranoid when they often say they find the Curia enthusiastically pro-celibacy for priests…