If the CPU is doing the work, then all the video card has to do is pass the signal along. So long as it's not like a defective contact pin or something so fundamental to the card's operation it can't do even that much, you should be fine.
For example, had a unit at work, been in and out several times. It is a unit from a line with a known issue with the graphics chip, and there's even a special diagnostic program to test for a bad chip. I ran one version of the test which works at just the bare metal level so to speak. No OS, just sending raw commands to the card. Those tests passed. Then I ran one that uses the OS so it can do things with OpenGL, and those failed miserably. So long as I wasn't trying to use the 3D functions of the GPU, it was fine, but when I tried using those functions, it wasn't so fine.
Depending on what part of the video card may or may not be bad, different things might set it off. Things that maybe weren't available in the stock driver, and were then done in software by the CPU.