Functional, yes, but probably not weapons grade. Tony originally used the repulsors as thrusters, it was only when he changed the settings during construction of the Mark III that he realized that they were a potent weapon as well. The Mark II was a test bed, and the implication of how Rhodey uses it and what Hammer does to it seems to be that it has no weapons or defensive tools whatsoever. And we never see Rhodey using the Mark II/War Machine repulsors as weapons, those two Bifrost-style explosions notwithstanding. And the Unibeam probably doesn't work either, even though we've only seen that used one or two times. Movie War Machine has effectively no energy weapons of any kind, and I'm only speculating that the Iron Patriot from Iron Man 3 has a laser based on how minimalist and compact the weapon is.

And speaking of Justin Hammer, that also explains the crap weapons War Machine had. That idiot basically strapped a bunch of standard-grade stuff to it, he didn't innovate or come up with anything special on his own. Most likely because the weaponry and technology simply didn't exist outside of SHIELD or Tony's basement, but we're still talking about a guy pretending that a shotgun is impressive when you've strapped it to the greatest tactical weapon in the history of warfare. The Mark VI armor is probably a more effective weapon than the War Machine, even when discounting that it's several versions more advanced than the base Mark II.

I would say that you have three alternatives, all of which are feasible for the movie's setting AND limited to something that the US military could come up with given the setting.
Idea 1 is a sort of repulsor cannon created by reverse-engineering the repulsors and non-functioning unibeam combined with Hydra weapon technology and based on observations of Iron Man's capabilities, substantially larger than Tony's handheld unit but also designed to operate at higher ranges and power, sort of like your plasma caster idea. This gives War Machine a "limitless use" weapon while also effectively being Rhodey's only energy weapon. It could even have a Hydra-style power coupler to homage the gatling gun's ammo feed, and emphasize how jury-rigged the whole project is.
Idea 2 is a laser cannon, sort of a larger version of Tony's wristie weapons, which I'm envisioning are one shots only because Tony didn't have time to fully miniaturize the weapons, and prioritized power and accuracy over reliability. Make the weapon larger, load the barrel with capacitors and cooling devices, and you could have a plausible laser gun that's not too much smaller than the prototypes we have today. Rhodey could even fire laser "pulses" or "beams" for different needs.
Idea 3 is basically a miniature railgun, not quite at the weapon phase but the solid weapon fits War Machine's modus operandi, and it feels like a prototype the military would bolt to this thing. It WOULD have limited ammo, but a railgun that small would also be firing small rounds, which could help in extending the meager ammo supply. This honestly feels more like a sniper's weapon, though.
Of the three, I prefer the first two. It feels a bit more like something the military of the setting would do, it's still technologically feasible given what we've seen, and it gives Rhodey a solid energy weapon (no pun intended).

I'm actually very curious as to what they're planning to give Iron Patriot in IM3, besides the back gun which I'm still pretty sure is a laser. He seems to have two forearm weapons that could be specialty load rockets, and I'm wondering if they've finally got the palm repulsors and unibeam working enough to be used as a weapon. Well, only six months before we find out.

And I'm sorry, this turned into a mini-essay. :\ I did not intend that.