When I purchased my T31, the dealer had no key (They inisted on calling it a 'blade'), but the fob.
They had to order me a new 'blade', and had to take a code from my other key/blade.
I asked the question on what would happen if ?I lost my 'fob', and they advised they could order a replacement, and program it to work with my X-Trail.
So I guess the answer to your question is, yes, but ask your dealer.