Not at all. Republicans have won the Congressional popular vote more times than democrats since 1992, and are about to win it again. There has only been one election since 1992 where Republicans won more House seats while losing the Congressional popular vote. They’re 2% ahead in the generic Congressional ballot right now. You can’t blame that on gerrymandering or whatever.
Republicans consistently lose the Presidential popular vote because their incentive is to run the most right-wing person who can win the vote that actually counts, the Electoral College vote. For Congress, republicans have to contest at least some seats in New York and California. But for the Presidency they don’t care if a single person in those states votes for them.
If we used a nationwide popular vote, the GOP would just run someone closer to the median of their House delegation, which consistently does win the popular vote.
To get an idea of what things might look like in a counter-factual world, look at this three-way poll in a Cheney/Trump/Biden matchup: https://www.prnewswire.com/news-releases/the-premise-poll-li.... Biden would get 36%, Cheney 20%, and Trump 45%. Shifting to a popular vote would move the coalitions around a bit: Republicans would have to care a little more about holding onto Romney/Biden suburbs. But it doesn’t mean consistent democratic majorities.