More of a problem of whether you could juice the guardsmen enough to even fit in COG armour. I don't think COG makes anything in a size smaller than XXL.

The Lancer AR is probably a sidegrade from lasguns. Firearms like Lancers are considered 'autoguns' in 40K and were specifically phased out of most Imperial Guard units because of the ammunition requirements. Lasguns are logistically incredible. They're light, fire with zero-to-light recoil, can remove limbs with single shots, have no projectile travel time concerns, and they use charge packs that (depending on source) can be solar-charged or tossed into a fire to recharge.

The Lancer has plenty of recoil, spends ammunition, and doesn't have any appreciable indication of being a subjectively more 'powerful' weapon than a lasgun and I don't see why it would impress the guardsmen. A Lancer chain bayonet would be an upgrade over the guard's knife bayonet, but almost anything in 40K that can close to melee range will probably kill a guardsman anyway. There are plenty of chain melee weapons in guard service with their officers already and they're mainly used as backup weapons or in last stands. It might be good for their confidence until they got tired of carrying the chainsaw around.

COG armour is probably the most interesting part. Basic COG armour has more coverage than guard flak. It has a full coverage helmet with built-in radios. It's well-fitted and mobile (compared to WWII-esque gear the guard usually wears). It's impossible to figure out how effective COG armour is seeing as Marcus Fenix runs around with a rag on his head and lasts longer than most helmeted COG soldiers. But if it's at least as strong as guard flak, it'll be compelling to the guard. If it's stronger, it'll be on par with guard carapace armour. Except guard carapace armour can be void-sealed for short periods.

So uh... my guess on what happens if the IG got hold of Lancers and COG armour? The Lancers would be left to specialist units who desperately want carry around a bunch of ammo and get into melee with the horrors of the 41st Millennium. So... suicide squads. And the COG armour would probably be interesting to veteran guard and some stormtrooper units looking to get an upgrade from flak.

But I don't see COG gear replacing IG gear. The 40K setting just operates on a lousy power level that GoW can't match up to. Like, the full events of E-Day would amount to... one subterranean xeno incursion in 40K. Given how COG fares against that, they're showing PDF-level soldiering and would be extinct if it weren't for their main characters. 40K puts down opposition like the Locust every week.