I've kept cigars in otterboxes for close to two weeks with no ill effects. Just like your home humidor, the better-humidified they are going in and the more cigars in there, the longer they'll stay. I also often place mine in individual bags before placing them in the travel humidor.
I would also be careful that the beads don't touch the foam in the otterbox, as I would fear the potential for mold if the foam got too wet.
Could you explain that further, how would the beads get the foam too wet?
the beads shouldn't have any moisture on them, though, only inside the crystaline structure, so it wouldn't be transfering the moisture directly into the foam any more than it does into the air; it wouldn't matter if it was in direct contact with the foam or not.
IIRC, even Mark has said that beads should be fine in direct contact with cigars. If having them touch the foam would get it too wet, I can only imagine what it would do to the cigars.
When I was using a 1/2 lb bag, I layed it directly on the wood. The only time I ever saw the wood get damp was right after I charged the beads; which makes sense as they would have still had some water on the outside of them.