I’m not super great with horary, so hopefully someone else can respond as well, but I think the answer is yes. Your son is ruled by Sun, which is strong in it’s own house and sign. The third house from him is his education and it is Leo — ruled by Venus in the third house. Sun conjuncts Venus, which I take to mean he will get in.
Again, I still think you should wait for other opinions, but if I may offer a suggestion, perhaps you can call the school or email them and explain that you are considering moving back and that you’d like to know if there is a strong likelihood of your son getting back in. Best of luck!