It might, it might not.
Depends on the programming and how exactly those are set to work. It seems like all three of those effect your character himself, not every single weapon. It'd be another damage amplifier tacked on the end of EVERY weapon used, if I remember correct. Another thread compared Hollow point bullets vs. Hand loader ammo, and it was said that the equation for damage looks something like:
(Base damage - ((DT * HP amp) - Your armor piercing value))) * bullet ammo amp * crit * headshot amp * Cowboy/Grunt/misc amp, etc etc etc.
If this were true, the amps would be tacked your damage at the end, after you've fired your weapon. Grunt cannot touch other game weaponry because it can't reference it. They can't add the K9000 to the list of weapons effected by Grunt because the K9000 may not be there when the game tries to reference it (as in you load up the game, it checks to see if the k9000 is there, doesn't find it, and thus can't apply the amp, because the game thinks the K9000 doesn't exist in your version. Trying to fix this in various ways could cause various problems). This however, if the above equation is correct? This is a very general, basic amp that's applied at the end of all of your damage dealt.
The easiest way to solve this? Grab someone with Thought You Died or Ain't like that now. Compare their damage or their firing speed with an AMR weapon to a character without it. Don't look at me though. I'm just Lucky to Be Alive.