Hi Devin,
The answer it your question is a qualified yes.
Technically, if you are currently enrolled in the Roman Catholic Church your Byzantine pastor would need to request authorization from the RC Bishop you are subject to to perform the wedding. That's a matter of paperwork and time, assuming that there are no obstacles to either you or your potential fiancee getting married.
Pastorally, the pastor of the Byzantine parish would expect (as a minimum): 1) you to be an enrolled and active parishioner for a reasonable length of time with obvious intention to live your life as a Byzantine and 2) your potential wife to be generally supportive of you living your life as a Byzantine and her willingness to raise your children as Catholics.
So it's possible, but up to the prudential judgement of your Byzantine pastor (no guarantees). And for an official reply to your questions you need to speak with him. I recommend meeting with him as soon as is possible to let him know your intentions so that he can pastor you towards a good marriage.
Prayers and best wishes,
John
