Heidi,
I used Aleene's Tack it Over years ago. I just went to check some unmounted stamps, to see how it has held up.
Not so good ...
Now I am not positive ... I faintly remember at some point Aleene's Tack it Over and Over was very hard to find. So I think I tried another glue?
So I can't be 100% positive it is the Aleene's that is failing.
Anyway, I have some pretty old Purple Onion unmounted stamps. I used Aleene's at least on some of them, and stuck them to a plastic binder insert (not a page protector). When I just checked, some are fine, and I think those are more recent ... , but some are horrible. The adhesive is brown and dry and sticks to the binder insert, but peels off the back of the rubber.
I don't know that Aleene's is worth the mess. I remember putting my rubber stamps on a foil lined sheet and painting the glue on with a foam brush and letting dry over night. You have to be careful to coat the entire back side, but not go over the edge to the front of the stamp.
At some point I gave up on that and started sticking my unmounteds to either cardstock (and then inserted in a page protector) or directly to the plastic binder insert with double stick tape. I peel it off and then use poster tape (doesn't leave a mess) to mount to a block or to a stamp positioner. If you're able to find the Sizzix Sticky Grid (I know, it's hard to find) that might work as well, though it is expensive. A roll of Scotch Poster Tape isn't cheap either ... but it works, or use regular double stick tape in your binder, and Poster tape on your blocks, for easy cleanup.
You might want to do a google search on Aleene's longevity before you invest the effort.