No, they wouldn’t.
Look at the math, Romney needs to win 49.7% of the delegates left.
If he wins California, New York and New Jersey (winner take all States that he will likely win), he would only need about 33% of the remaining delegates to clinch.
With Gingrich keeping his numbers down in the proportional States, it gives a chance to keep Romney under that number if Santorum can win the winner take all States of Texas, Illinois, and Pennsylvania.
If Gingrich gets out, Romney will pick up 1 or 2 or 3 extra delegates from all of those proportional contests. And if that happens, Romney absolutely gets to 1144.