Absolutely no way would City get relegated. Think about it, Juventus got caught bribing referees and that was a relegation offence (plus they lost some titles they'd won). If (big IF) City are guilty it is of 'bending' rules rather than fraud and I think in that case a points deduction and maybe a season out of Europe is more likely. Their alleged offences are nowhere near as severe as what Juventus got found guilty of.
I just want to reiterate this is a big IF, I have no idea whatsoever (like everyone else here) if City are guilty of anything, I've no dog in this fight as a Gooner but I wanted to state that it would be illogical to relegate City IF they were found guilty (bear in mind there are 115 charges to go through) given the precedent of Juventus, also it makes no commercial sense for the PL to do it given City's status as a crown jewel for the PL's ability to monetise its product around the world (let's face it, the PL aren't selling TV rights to Thailand because the locals want to see Carlton Morris score a deflected goal for Luton, they want to pay to see the very best players play amazing football).
Also I'd take no solace in City getting done - winning the league in a season where the main rival had a bunch of points deducted would always have an asterix against that achievement. I guess Man United fans would happily take winning the trophy that way but I'd not view it as a big achievement if my side won the league by finishing 10 points ahead of City where they had 16 points deducted. It would be totally hollow.
But to sum up, City aren't getting relegated for this even if they were found guilty. It isn't really in anyone's interest to do it from a commercial perspective, it would devalue the PL massively.