Absolutely.
Not only would the Cowboys be 4-1, Dak would have laid at least 30 on a couple of those teams.
Unlike those who disagree, I'm going to offer a reasonable explanation for that belief,
First of all, same Cowboys defense regardless of the starting QB. This is important because it was the defense that won the game, not the quarterback. As such, Dak would only need to score 18 points at the most, in each game.
The Cowboys would still have the same kicker, Maher influenced the outcome of the game more than Cooper Rush
Last season the Cowboys under Dak scored an average of 32.5 points. So basically, we are asking if Dak can score a little over half the average points from last year.
Also Dak has the Commanders and Giants number. He is 9-2 against the Giants, 9-1 against the Commanders.
Against the Rams, the Cowboys offense didn't get on the field until it was already 6-0 in their favor and that drive started on the Rams 20 yard line. The Rams only scored 10 points so with only a half of a quarter played, Dak would have to find a way to score 2 points in order to win.
In order to get a more realistic perspective, we should ask ourselves what Cooper Rush did for the Cowboys to win 4 straight and then compare that to Dak's last four starts.
Last Four Starts
Cooper Rush 65-115-775- 4TD-0INT
Dak Prescott 87-133-985-12TD-1INT
There is nothing to indicate that Dak wouldn't have the same record for those four games, quite the contrary. It wouldn't have been close.