Primarily, you should follow what Laurence said, which is to play clean and accurately.
To answer your question, I think that it is of course helpful to push the tempo a bit faster as some songs require it. For example, Beethoven's Moonlight Sonata - 3rd movement.
The benefit of pushing the tempo is that you will be able to play other pieces much better, as most pieces incoporate scales/appegios, so playing it faster will make playing scales fast much more comfortable as you're more familiar with it. Besides, there's only a certain number of scales on the piano, it's not like chess where there are an infinite number of positions. You'll definitely come familiar scales that (by that time) you'll have managed to play it at a high speed.
Try to push the tempo if you're playing clean and accurately at the current tempo you're at.