No. Please do not set up two different login accounts in HUFP. If you hold a valid HUID you should use that information to set up a single HUFP account.
The option to log in without HUID credentials is a recently introduced system function. It was created to enable applicants outside of the Harvard PIN system to apply for certain opportunities that, if successful, would bring them to Harvard (Banting Postdoctoral Fellowships, for example).