I’d say it would depend on how tight the trigger guard pin is. I don’t think you could drive it in to the plate, but you MIGHT (MIGHT) be able to reach behind and push it foward. I don’t think it’s possible myself.
If I wanted to steal the rifle, I’d just put a crowbar behind it, drive between the drywall and plate, and pry the whole shebang out. Most burglars are not going to take the time to use a bent paperclip, just a small crowbar, and unless you have steel studs, it will just pop out of there.
There will be plenty of clearance to get a bent paperclip, or even a formed wire hanger in there, and the spring tension is not that much. You do have to pull it outward from the wall. Anybody that knows an AR could have it in seconds.
A crowbar braced against sheetrock will make exactly no progress against a plate bolted into the studs, and I’d have more confidence with wood than steel ones.
It may not keep the gun from getting stolen, but it may just satisfy “safe storage” laws/regulations in jurisdictions that have them.
Like any trigger lock or cable lock, it is more to satisfy a legal requirement and keep little kids out than to provide real security.