It should be fine, Steve. Just fasten it in place somewhere and spritz it with water if it doesn't rain.
These things grow naturally here and get blown hither and yon during storms then re-root and carry right on. The roots really just serve to hold the plant in place, they don't feed or gain water too much. Being epiphytes, they gather all the goodies through the leaves. So as long as it has some green leaves, it will re-attach where you want it if you just anchor it for a while.
Oh, and get those little Tigers a fluffy ball to play with, maybe?? Love cats!