That's honestly a great question. I don't know how relevant this is, but when I was talking to the program admin for MDS, he said that transcripts can be sent later on to him, if there are any updates. So I think, if you officially submit your application without your letter, you will have to forward it to the NPSIA admin and can't change it in the system yourself.
But then again, the statement of intent is the main part of your application, other than your grades and references. If I were, I wouldn't risk.
Good luck with your applications!