No.
How could it? The laws of physics are the same in every inertial frame. There is nothing special about our laboratory frame. In its rest frame it is simply a proton just as before.
There could be proton decay, of course, but I guess that's not what your question is about - if it exists it applies to all protons.
In our lab frame, and assuming protons decay at all: Sure. Not that it matters, their lifetime is so long that we won't see a decay in accelerators anyway.