Dear student

This is a normal approach. Many students apply in schools as private candidates and meanwhile do coaching for competitive exams. You can apply for neet. There's no problem in this. In your application form you can fill the name of your school and there's an option to apply even if your results are not out for class 12th. You can update your marks after the results. But see that you fulfill all the eligibility criteria. Go for it.

All the best.