Are you asking to simply embed a web page in a finesse gadget, which requires a login? Or are you asking if you can pass the finesse login credentials through to that embedded page? If the former, then yes, if the latter, then no, I don't know. That's an interesting idea, and I would be curious to know that too.
There's actually a thread in progress with someone else trying to embed a web page in a finesse gadget:
https://community.cisco.com/t5/contact-center/finesse-screen-pop/m-p/3752963Maybe that will help hump start your progress.