Hardware acceleration gets your gpu to help your cpu.
I've got no idea why you would have that 'on' for watching YouTube videos. Or even what software that you would have it 'on' in.
And I gather you are watching movies while you game. Which will add more load to your PC and so your game fps will decrease.
Instead of 'felling' like you're only getting 20 fps why don't you use fraps to see what you are getting.
I don't watch movies, I was using netflix as an example. I usually only watch Twitch which uses Adobe, which has hardware accel.
And as I stated, I am getting 40, then it bumps down to 20 with videos running. When the framerate does not go down, it feels like 30-40fps.