Theoretically yes.
Logically the only difference between web and extension is the method to get the user’s Twitch ID.
However on web you won’t be able to use the Twitch Extension helper, which’ll mean a bit of restructuring if you are trying to use identical code.
I run an extension that has a website where people can perform the same actions as in the extension. Both do their respective oAuth/TwitchID dances and then talk to a common API, and different display functions display the data.
So, yeah I have a common User data, but the frontends are completely different