I have a similar setup to this for my house office. I use an HDMI over ethernet extender (with USB), and put my tower in my computer room in the basement. This way, it is all neat and tidy in the office. I only have a single monitor in there however, a 38" Acer 3840x1600 (@75Hz). I play games just fine, although I never actually tried to see if there was any lag or anything of that sort. The only point of reference I have is my office speakers, which are also wired all the way to the basement and I don't really notice any sync issues with video/audio. Depending on how you perceive visual/audio data however, YMMV.
Also, when I had my house built, I had them use CAT6A so bandwidth isn't an issue. I think CAT5e would still work just fine (depends on run), but anything below might be iffy.
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