When I had FAL's or L1A1's the carry handle was more of an annoyance than a convienance. When doing any sort of patrolling practice out here in the Ozarks and I removed them and lucked out with my last L1A1 I owned never had one on it.
Plus it promotes bad weapon handling habits, IMHO. As in not having the rifle at any ready position.
On something like a SAW or GPMG I can see it but not on a regular rifle.
I did notice your location so it may not be as much of a concern with it getting caught up in thick brush or having soemthing slap against it and make more noise as here though.