Does the frame on a bike make the bike go faster?

Well, if you didn't have a frame at all, there wouldn't be anything to tie the parts together with. And a pile of loose parts on the floor wouldn't be going anywhere, at any speed.

So the question only makes sense if you compare different frames to each other. A lighter frame will make the bike accelerate faster but won't really do anything for top speed. A stiffer frame can make the bike handle better, which might mean that you dare to ride it faster. A stiffer frame can also do a better job of getting the power into the ground, again improving acceleration.

At the extreme end some frames can be more aerodymanic than other, also improving top speed a tiny bit.