tl;dr - No.
Only 9 teams in history have made the playoffs with a negative RDiff. Three of those teams were in 2020, and a 4th team was in the strike-shortened season of 1981. Of the remaining 5 teams, the best record was 90-72, shared by the 2007 Diamondbacks (-20) and the 1997 Giants (-9). Neither team lead the league in wins.
Source:
MLB.com: Playoff teams with negative run differential