You can: Today, playing locally on a PC, your latency is one hop to/from the game server. Playing on cloud, you have one hop to the virtual PC, then an extra hop from that to the game server. Combine those two hops, and the latency should in theory be the same as with a local PC and a game server. But it'll be a different kind of latency, showing as input lag rather than a delay in interacting with the other players.
About crowd-drawing games, looking at the top list on Twitch, probably more than half of them don't require super low input lag. Csgo does for sure. Valorant, Apex, Fortnite, and CoD are less precise, so I'm not sure. The rest aren't shooters.