Yes - I would think a muggle would have that similar protection. Dumbledore is well aware of the "magic beyond that taught at Hogwarts" or something like that - i.e even muggles/non-magical people are capable of some things that transcend the muggle/non muggle divide...JKR's appeal to a "common humanity"?
An interesting thought. I was re-reading Book 1 - and thinking; could Quirrell have formed a horcrux during his time at Hogwarts, so something in the DaDA office could be one? We know Hogwarts IS extremely safe... Another element - could Quirrell be considered a horcrux, since he apparently let Voldie's "soul" in? Worth thrashing out, esp. since the Riddle diary was a Horcrux and that is from a previous book. Depends on whether you'd think Dumbledore would overlook that though...