2GB and 4GB GTX 670s in SLI?

Will a 2GB GTX 670 work with a 4GB GTX 670 in SLI?  Correct me if I'm wrong, but from what I understand, it should work; however, it defaults to using the lower amount of VRAM of the two GPUs.

The reason why I'm asking is because I currently have a 2GB GTX 670, and I was planning on grabbing another GTX 670.  If I did grab another one, I figured I would just go ahead and grab the 4GB model.  I have a friend who may buy my 2GB model from me.  If he did, I would just use that money to buy another 4GB model.  And then I could run games such as Skyrim on ultra settings with high res texture mods.  With my current setup, I occasionally dip in the 30 FPS range and I can definitely tell when it does.  It stutters and the gameplay isn't as smooth.

From what i understand, it will work but both cards will run at 2gb.

if you sli those you're gonna get just 2gb.

Yes, I know.  I just wanted to know if it would work.  Thanks for the info.

[Edit]

I did a little research, and it turns out that it can't be done.  Lots of people are either saying no or they are giving an iffy yes.

http://www.overclock.net/t/1409979/solved-can-i-sli-a-4gb-gtx-670-with-a-2gb-gtx-670/10