Yes, I tried the slideshow, but it does not go to full screen on my mobile devices. On my desktop pressing the F11 key gives full screen during the slideshow.
I think the short answer right now is "no", but there may be other browsers like Firefox or Opera that can on iOS.
Mobile Safari doesn't support fullscreen yet. One trick that works on my phone is rotating from portrait to landscape mode. I don't think this will work as well on iPad but the rotate trick might improve things. I was hoping that Chrome would work since there is a fullscreen option on Android, but it looks like they don't have the same support on iOS yet. If the browser does support fullscreen, tapping on an image in the slideshow mode should show a fullscreen button next to play/pause -- that's what I see in Android.
Thanks for bringing this up though -- I think there might some room for improvement here so we'll update this thread if the situation improves.