Yeah, I think the GPU is more important. The monitor can come later. So if I use the GTX 670 on my 1366x768 res monitor, does that mean it's easier to let me play games most games, if not all, on ultra-max settings easily? Does it have any negative effects? Also,I read somewhere you could 'bleed' your GPU out. Assuming it's easier and isn't utilized to it's full potential like on a 1920x1080 monitor, I heard the 670 lasts longer before needing an upgrade compared to using the 670 on an 1920x1080 res. Is that true?
A GTX670 can max almost all games at 1080p. If it's 1366x768, then it's not even a problem. I'm not sure what you meant by GPU bleeding out.
On your last question, it's not true. I don't know who told you that but don't believe it. It'll last the same either way. The performance of the 670 will last you longer without needing to upgrade than lower end cards though. However, these days any mid-range cards and above will last about 3 years at "reasonable" settings and can still maintain respectable framerates in most titles.