I have no doubt he can enroll in public school. I have more doubt that if he does he’ll be able to graduate in May or June. Public schools often have requirements like sex/health ed/speech/PE, etc. that private schools may not have. Some may not give credit for courses at the private school for which the public school doesn’t have an equivalent. And it may not be that easy to be plunked down in ongoing classes and pass them.
Again, I think the MOST important thing is to see that he graduates from high school this year. If his admission is rescinded, he can take a gap year and then reapply. While many colleges accept GEDs, not all do. Not all employers do either. It’s MUCH better to have a high school diploma than a GED.