I have known kids who had a rocky transition to a grade level, applied out, and things were better by the time they were in a position to make a choice. Or who had a rocky year with a bad teacher, and decided at the end to apply out the following year, and then got a great teacher the next year and decided to stay.
I will say, though, that so much of a kid with disabilities experience at school, especially private school but in public too, has to do with the degree of teacher buy in. If a teacher believes that kid shouldn't be in their class, or would be better served elsewhere, they often aren't going to problem solve well, or will do subtle things that kind of sabotage a kid's performance. Many teachers in private believe that schools for kids with disabilities serve students perfectly. If they have a kid who struggles a little, and is applying out, their internal narrative might be "This poor kid, and his poor parents. They're trying so hard, I'll do whatever I can to support him while they figure it out". If that kid comes back, that narrative might shift to "I can't believe they made that decision" and they might either consciously do less "If the parents aren't doing right by their child, why should I do extra work to compensate" or subconsciously "He doesn't belong here, he belongs in that school they applied to, that's why he's struggling, I won't change anything because there's no point, his struggles are because he doesn't belong here", or even "They obviously didn't realize how hard things are for us with him here, I'll do things that will highlight the struggles, and then they'll make the right choice."
You might think that you could get around this by just not telling them your child was accepted but then it's easy to become "If X school thought he was too disabled to be there, then obviously he's too disabled to be here! What's the point in problem solving".
So, I'd be aware that applying out and not going can have negative impact.