Bearing in mind the good points that JackNaylorPE brings up, some paint is conductive, some paint is not. So, long term effects notwithstanding, short term effects can go from perfectly fine to not working at all, just based on the paint you use.
While the warranty on your old graphics card may be long since expired, I doubt any manufacturer would honor a warranty on a part you have spray painted, so I would not modify parts still under warranty without first accepting the loss of the warranty.
I have both plasti dipped and silicone coated PCBs in the past without any ill effects, but they were not heat sensitive applications. Obviously any electrical connections or heat transfer surfaces need to be masked from any painting or dipping you may perform. I would certainly not coat anything subject to constant high temperatures, as nobody needs to breathe half-melted toxic substances that might be released by standard spray paint being heated, unless you choose to use a plasti dip or high heat paint, both of which tolerate the temperatures they will be subject to in a standard PC application.
Yes, you can paint heat sinks. Yes, cooling efficiency will be decreased on a painted heat sink, so only do this if your heat sink has enough extra capacity that raising it's temps by ~10°C won't put you over any thermal limits.