This is certainly possible. You can force the gallery to always be displayed in Small Screen Mode (where thumbnails and main images are displayed on different pages) by setting screenMode="SMALL"
The problem with this answer, as far as I'm concerned, is that small screen mode isn't really suitable for large (i.e., non-touch) screens. The fact that this is possible in small screen mode, though, makes me think it might not be that hard to "fix" Juicebox to allow for this. Rather than start another thread, I thought I'd put my $0.02 worth here.
What I'd like is the option of having that second page, where thumbnails are displayed, just as they are in small screen mode, but without all the other "small screen" changes. The only real problem I see is that the "small screen thumbnail only" page has no mouse navigation. That is, on my workstation, with my gallery in small screen mode, I get 8 rows of 17 images (136 images). If my gallery has more images than that, at the bottom is says "1 of 4" (or however many pages there are). But I don't see any easy way to get to those other pages. If I click on the last image on the page to bring up the single image, advance to the next image, and then return to the thumbnail page, I get the second page of 4, but that's not really a suitable navigation method.
So, my feature request would be:
Add an option to large-screen mode that displays the Show Thumbnails link that will bring up a page of thumbnails (as in small screen mode but without the other small screen features).
Add navigation to that thumbnail page in large-screen mode.