Depends. Some Atari 8 bit games used the display interrupts for timing, so those could run as fast as possible so long a the display interrupt happened at a consistent 60hz. (now that I think of it, I think some games has issues in countries with 50hz updates)
This is true for a lot of older and simpler games for the C64 as well, but at the same time for most of them you'd see absolutely no benefits, since it's common for everything to hang off the interrupt.
A few games that glitches when there's too much stuff going on at the same time might run smoother.
Demos are likely to mostly not work because any remotely fancy effect tends to depend on much more precise timing, though.
There’s plenty of games and demos that require the exact amount of raster time to function. If you want to display things in the left and right border you have to switch something at exactly the time the graphics chip is displaying the right border. That’ll never work if the timing changes.
