I've loaded and fired .44 mag with LRP's before just to test and see. The primers sat significantly proud of the case heads. I single-fed them into a lever rifle. I was extra gentle when chambering but didn't notice anything abnormal feeling. It worked, all the rounds went bang, but I have no plans to do it intentionally again.
In a revolver cylinder they'd likely jam the cylinder from rotating because the primers stick out so far.
There is a chance they may cause a magazine/cylinder detonation under recoil if in a tube mag or more than one is loaded into a revolver. I'd hardly call it a guarantee and certain firearms may be able to shoot indefinitely with significantly proud primers without a detonation but it's an easily avoided, pointless risk no matter how small.
If the primer pockets were deepened with a uniforming tool to rifle specs, and the hammer was known to be strong enough to set off a rifle primer, there would be no risk but then you need to carefully segregate your brass which is tedious and not worth the effort.