ouais t'excites pas mon bo, je voulais dire 680.. tu le sais puisque t'as l'air au courant.
I am also an user of GTX570 SLI.
Going from GTX570 SLI to a single GTX680 will bring a performance dip most of the time. Whether the dip is small or moderate, it varies from game to game. However, at OP's 1080p resolution, the fps should already be quite high so that any dip will not make much practical impact. As the ultimate goal (hopefully) is to get another GTX680 down the road, there will be a performance increase at the end. But again, that increase might not be too beneficial as the fps is already quite high at 1080p.
This leads to my main point:- upgrading the current Acer H233Hbmid 23'' 1080p monitor is a preferred path of upgrade, IMHO.
If staying with a single monitor, upgrade to a single 27 (with either 1080p 120Hz or 2560x1440 60Hz) or even a 30 is a worthy consideration. IMHO, GTX570 SLI or GTX680 (and SLI needless to say, of course) has more than enough power for 23'' 1080p, in general.