Nah, most will be Honorable, General (under Honorable Conditions), or at the worst, Under Other Than Honorable Conditions (which isn't a good one to get, but better than a BCD or dishonorable; OTH can still be eligible for VA benefits depending on their circumstances), and then an Entry-Level Seperation for people in boot camp/basic training when the policy hits.
I'm sure that some transphobic commander somewhere might delve into the UCMJ and create some trumped up charges to try to court martial a trans service member whom they dislike and want to make an example of,mouth it probably won't be common.