In theory yes you could feed just timothy grass. However in practice it is a little more complicated then that.
First problem is if the guinea pigs are not used to eating fresh grass eating moderate to large portions can cause gas so you need to slowly increase how much grass they are getting. Second problem is growing enough grass to sustain them, it might be quite a bit more than you first anticipate, you will need a large area to grow said grass. Third problem is keeping up the supply all year round, there is a reason why hay tends to have a growing season, and if you change them back to hay then back onto grass you are will be back to the first problem. Fourth problem is fresh grass decays and contains moisture that can lead to mold growth so you will need to frequently remove all uneaten grass from the cage and replace with fresh grass, but they will still need unlimited grass 24/7 if using it as a hay alternative.