I think if you got the APK from somewhere reputable it would probably work - I’m not sure that Monzo actively blocks this sort of thing.
But two thoughts / issues / questions:
- Does Monzo rely on Google Play Services (or similar) to run? If so, this won’t work.
- Would you really want to trust downloading an unsigned APK from the internet? If it were a direct download from Monzo, sure, but I’d be very worried about third party ones, personally.
tl;dr: will quite possibly work but 
at your own risk