No. The refresh has nothing to do with how it looks. High refresh and a lower response reduces possible ghosting effect you may see while moving quickly on certain screens. Anything pretty much below 8ms in my experience is fine, even @ 60hz (typical panel). That has no effect on actual graphics or game looks though.
The point of having a higher refresh is based around 2 things for gamers. Vsync, and 3D. When using a 60Hz panel applying Vsync to a fast paced game can cause input lag. It may be minimal but some people are good enough to notice it. I typically run Vsync with everything except BF3 because I notice the lag when playing online. (Not to be confused with any ping lag, your PC has nothing to do with that). The cause of this, is because the vertical sync limits your FPS to 60 causing things to be "held back" in simple. This causes some input lag. Now that is a very simplified definition, so hope that works. When having a screen that is 120Hz or higher you have support for 3D and that FPS cap from Vsync is raised to 120 and 144. So, if you buy a 144Hz panel and enable Vsync on a game you have a height of 144FPS to achieve before there is any limitation. If your card is only capable of outputting say 90FPS at max settings on a particular game you will experience no input lag thus being able to reap the benefits of Vsync which reduces any screen tearing.