Hello, I hope you are doing well

Yes you can appear for UPSC examination after getting into NDA. The basic eligibility criteria to appear for UPSC is that the candidate must hold a graduation degree in any discipline and from a college recognized by the government of India. The candidate must be a citizen of India and must be at least 21 years of age and the maximum age must be 32 years for a general candidate. There is some relaxation in age for OBC, SC and ST candidates.

But, the main issue is you can't just get a leave  for your exam from your job for complete 1 year as you will have to give a good amount of time to the preparation of Exam.

Your option could be to leave the job aside and focus on UPSC or you could take a premature retirement which I don't know is actually possible or not because it is not yet confirmed which force you will join after clearing the NDA exam. The time period for premature retirement is different for different armed forces, also your retirement would have to be approved from the respective authority.

Hope this helps