Would it be possible to run the resolution at 1680x1050 when I first get it?
Will it squash and distort the picture?
My system will be using a single Gigabyte 6850 HD 1GB video card, and I would like to squeeze as many frames as possible until I can afford to Crossfire and not have to buy a new monitor to get the max resolution from them.
since 1920x1200 is that monitor's native resolution you really should use that. this should be your desktop resolution. it would be recommended to lower quality settings and stay with your native resolution but the following ideas do work.
from the in-game menu you could set the resolution to 1680x1050 fullscreen. most games will run when your in-game resolution is different than your desktop-resolution. be prepared to have a few icons shift on your desktop though. i've only had one game refuse to run at a resolution different than my desktop (guildwars)
I still play older games ( starcraft, unreal tournament 2004, etc..) and not all of them support 1920x1080 (my resolution). most games have an option close enough that no distortion is noticed. some old games with a much different aspect ratio (4:3 maybe?) run with black columns on the sides.
You should get around 50FPS with modern games, full resolution and high settings with that hardware. I can't really see why you'd want to go with a poor image quality. Is that a 120Hz monitor? If it isn't, going beyond 60FPS doesn't bring much benefit anyway.