Yes because if everyone has variant A and variant A provides some kind of immunity to variant B then there will be less reproduction of B and therefore the chan

Yes because if everyone has variant A and variant A provides some kind of immunity to variant B then there will be less reproduction of B and therefore the chance of mutation becomes lower even if B infect everyone at the same time too. But this is only true if you expect both A and B to reach everyone eventually. Currently we expect that a lot people never had any variant and therefore no mutation could happen in these people. But if they get it all eventually then it just delays mutation.