That’s not how employment NDAs work. They never forbid a candidate from disclosing that they worked for a company and the general nature of their work. They just forbid the candidate from talking about specific knowledge gained at the company.
Do not use this excuse because it’s an instant red flag for anyone who knows even a little about the hiring process.
I’m sure that the admission staff will take your application very seriously if you claim you were James Bonding it up for a few years.