Yes, this works! I just tested this as I was curious myself, and when Safari asked me for Touch ID my watch would also give me the option to authorise a sign in.
leonkoole
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Ah, thanks. So a user event is required to use Face ID or Touch ID. That answers my question, so I guess I'll have to work around that limitation, if there even is a working way around it.
I think you have to enable "When Authentication Local Authenticator" under Experimental Features in the Develop menu.