Technically the s6 is smaller than the s5, but I read on the specifications page that s5 is the biggest they will allow. I've asked around and heard that the s6 will not fit.

Also I'm wondering how an s6 edge might work. If I get a new smartphone it would definitely be that one, but would the "edge" not work with the pipboy?

Can anyone confirm? I'm googling around but can't seem to find a direct answer.

Dont think so no.

http://www.ign.com/videos/2015/06/29/fallout-4-pip-boy-restrictions-and-the-division-beta-details-ign-daily-fix

http://www.bethblog.com/2015/07/01/fallout-4-pip-boy-edition-available-again-for-a-short-time/