Do screen resolutions affect graphic cards performance?

Solution
The answer to the title question is YES, and its a GREAT amount. That is one of the biggest determining factors in which card you need to get.

Depending on what games you want to play (or if you even want to play games), and if you want full details a 4670 will not get you very far! The lowest I would recommend is probably a 5770.
Screen resolution significantly affects graphical performance. As to whether the 4670 will be fine depends on what you are planning on doing. If you are just going to be doing basic office tasks(word, email, web browsing etc) it will be plenty, if you want to do gaming its going to be weak for 1920x1080 and would be restricted to low or medium detail settings.
 

Helltech

Distinguished
The answer to the title question is YES, and its a GREAT amount. That is one of the biggest determining factors in which card you need to get.

Depending on what games you want to play (or if you even want to play games), and if you want full details a 4670 will not get you very far! The lowest I would recommend is probably a 5770.
 
Solution
Yes, Screen resolution has a massive impact on performance, obviously the more pixels the GPU has to render the longer it will take to render the entire frame so you will end up with less FPS (Frames per second).

Higher resolutions (Like 1080P+) require more VRAM (Video Random Access Memory) to store all the textures in the game, the HD4670 you linked to has 1GB of VRAM which is good, but unfortunately doesn't really have the raw power to be able to play the latest games at decent in-game settings.