There are several considerations mostly based on your floor covering requirements.
As long as the screws are flush with the underlayment you should be fine. However, depending on the floor covering you may have to cover the screw tops with a filler. Some floor coverings only use adhesive around the outside, others need the whole floor covered and a super smooth underlayment nailed.
I screwed an underlayment to the floor of our kitchen remodel one time, remarking to my wife that I pitty the fool that had to take the floor up as I went heavy on the screws. To make a long story short, I was the fool! We changed our minds on the floor covering before the job was done, the new one needed a super smooth underlayment. Still using used screws here and there!