Lemme share a little story about graphics and immersion.
This one time I lost myself in Advance Wars: DS, with the animations off. At that point, the whole game is just these blocky little sprites shuffling around on a big ugly grid. I was so into it that I literally had no idea what was going on around me. I'm lucky I didn't miss my train stop. Obviously, the graphics were terrible; it was the game itself that was so engrossing.
I know this is just me, though. Many other people seem to care a lot more about visuals.