Definately - if rolling around didn't waste time then most of them wouldn't do it
Yes they would, firstly sometimes players are hurt, regardless of playing on or being fine. Have someone kick you really hard in the leg, see if it stops you doing what you were doing and if you're fine to go back to whatever you are doing 2 minutes later.
People have recently decided that if you don't go off on a stretcher unable to continue... you're faking, it's ludicrous.
Second, people often time waste because they are under pressure and want to relieve said pressure. With a clock on the game there is pressure to restart the game from both the ref and the player rolling around as it can be say a team 1-0 down with 10 mins to go, he wants to get the pressure off after 5 corners in a row, but they still need to score. This can get actually hurt players still in pain to get up and continue also.
If there is no actual time lost, and no penalty because the ref just stops the clock, then players have less pressure to take as little time to recover as possible. Actual time wasting or proper dives(where there is no pain or injury involved) have no reason to get back up quickly. The ref loses his ability to give out cards for time wasting as effectively no one is losing if the clock is stopped. it lets those who want to break the momentum in the game do so much more easily.
All in all, there are no benefits, it's completely pointless and there are as many potential downsides.
Football HAS always and WILL always have breaks in play, get over it, there is nothing wrong with it. Divers need to be punished for diving, time wasting should as it is now, be punished(but with refs being better about it), fans need to be less ridiculous. It's okay to take 15 seconds over a throw in when it's 0-0, but when you're 2-0 down you scream about the same time span as blatant time wasting.
The only thing that needs changing is better decision making, which comes from video replays, nothing else.