I don't think it will be a problem for PSG if Mbappe leaves in Ligue 1. But in the UEFA Champions League, They will face big problems. They have a match with Real Sociedad in the UEFA Champions League and I think without Mbappe they will struggle against them. PSG has achieved a good lead and I believe that would make them comfortable in Ligue 1. If they had not had that, they probably would have been in danger.
It will indeed be easier to be eliminated from the Champions League if players like Mbappe leave PSG in the transfer market this month, because now PSG is in need of several players like Mbappe, although not only for the front line. In the Champions League, PSG have never succeeded in winning a trophy, so this season will really be difficult if a player like Mbappe leaves PSG and there is no more worthy replacement.
But to be honest I don't see Mbappe leaving. Because if he were to leave, we already would have heard some rumors by now. Real Madrid also said they wouldn't be buying any new players, so Mbappe wouldn't be joining Real Madrid. And I don't think any other team can afford him.
The rumors are not yet visible, but who knows in the next few days it will be if Mbappe really wants to leave. However, if Mbappe himself doesn't want to leave or the fee for being approached by another team feels too big and expensive, maybe that's what's keeping the rumors from surfacing now.