Dual monitors, single card, hightest resolution question

I'm building an i7 system and want to drive two 23" monitors that have resolution of 2048 x 1152 each using a HD 4670 1gb card with dual dvi outputs.

When I set up the single desktop across both monitors, will I still have the 2048 x 1152 resolution on each display? In other words is the actual virtual desktop now 4096 x 2304? If so, do I need a card that will output 4096 x 2304?

I'm imagining that at 2048 x 1152 on a single monitor I probably can see almost a full page say for example in MS Word from top to bottom at 100% and much of a web page from top to bottom. So, when I add the second monitor, will that Word page still appear the same so that I can drag it over to the right monitor and open a full web page on the left monitor?

Thanks in advance?