would it be okay to run a fairly average PC without a case fan? i'm building one for my grandad and its significantly quieter without the fan (and noise matters in this case, as it'll be next to his TV and on most of the time) but if I leave it out is it likely to overheat after a few hours or something?

make a hole on top of the case so hot air scapes

This is probably a bad idea if the fan is part of the design. You'd should just buy quieter fans if the noise is a problem, or get your grandad headphones for his TV.
If going ahead, make sure you set the bios to automatically shut off when it reaches a certain temperature to avoid damage and FIRE. And check the batteries in his smoke detector.

I don't expect that your grandad will be running any stressful software, so I think as long as he doesn't leave it in a dusty corner where there's no airflow/cover it with clothes or etc, it should be fine. But if it were up to me, I'd install one rear exhaust fan, and use a fan controller (such as Zalman fanmate) to set it to a quiet speed.