If the address registered for your account doesn’t match the address the credit agency has for you then it won’t show.
Monzo currently only shows on Noddle/Call Credit.
I think you can get a linked address on your file, but I’m not sure how that works.
In terms of issues, it won’t be an issue for your friend. The possibility of not having a bank account on your credit file being an issue is one that is being discussed still - Monzo NOT On Credit Report