I dont know about Zagg but I got SGP STEINHEIL ULTRA CRYSTAL and have no problem, I also emailed Zagg and asked the same question they said it should not be a problem. BUt I only asked about screen protector not full body.
I had this setup on my bb. Different device but same case and an is. You may get some small ripples after a while on the edges but since the case snaps over the shield you won't notice them.
I have full body Zagg and the Seido Innocase on. It fits. Barely. Its a struggle to get it on or off. If you're one a constant battery puller or you switch out SD cards a lot, it may be a problem.