If I decrease my screen size will my frames per second (FPS) increase?

[Kappa]

Yes, let me put it like this:
Larger picture = more pixels,
smaller picture = less pixels,
less pixels= the less your GPU will work causing increase of FPS
I seriously don't know why EpicHwang thinks that you'll have better FPS with better internet, I have in a game called DayZ like 300 ping which is basically your connection (the more you have, the more lag you'll get), I was lagging like hell of course but my FPS were always at 60 FPS I didn't get lower FPS, I changed to a server were I had like 20 ping and the frames were the same, so no, better internet won't give you better FPS.
If you want more frames, you can either lower the size of the display you're playing, get a new GPU or lower the settings.

So returning to your question, yes, if you lower the size of the screen you'll definitely get better FPS, you can also play in the 33" inch TV and lower the resolution in the game