In terms of speed SQLite is far superior, because it is essentially a database file that is being directly accessed. MySQL on the other hand is a service, a process that handles and manages data, as well as offers applications an interface to read/write that data, so there's bound to be some delays.
In terms of running a server that uses a website for account management, using SQLite is not a very good idea since it requires some rather sophisticated methods to properly access the data (Sockets).
This also raises a lot of security concerns.
So in the end... Is it possible? Yes.
Is it recommended? Definitively no.
Last I checked GeisorACC was the only web account management system that could handle SQLite files, but from what I've heard, it's full of security glitches and issues that may or may not compromise account security.