your panel resolution will not change. it will still be 1680x1050.
however, your "total resolution" will change.
for example, if you bought another 1680x1050 monitor and placed it side by side with the monitor you are using now, and changed the settings so that it extends your windows desktop your screen real estate is 2360x1050.
if you intend to play games across both monitors then you might want to check your video card to see if it is powerful enough. other than that, rendering the desktop/webpages can be accomplished one two monitors with a low end card.