It wasn't a large project migration, but I do have experience of a small/medium sized project that was started using both WebForms and MVC - the WebForms part from an existing CMS, and MVC for new bespoke development.
I didn't see very many problems. The main problem that I remember was keeping track of pages and routes - adding a SomethingController would cause all the WebForms pages in the Something directory to become inaccessible, for example. So it's definitely worth planning out in advance all of your URLs and partitioning them between WebForms and MVC. Having overlaps isn't impossible, but it does need some care, and proper testing.
It was in my last job that I did this, so my memory might be a bit hazy on the details. Authentication wasn't a part of this particular project so I'm not sure how that would work, although I can't think of a reason why it wouldn't. So, sorry I can't give a definitive answer to your question, but I hope this helps.