Well if you suggest that you wish to run a node with that PC then it would seem more of an enthusiastic act than attempting to mine with a GPU given the current difficulty level of the bitcoin Blockchain. Well as at around 2009 - 2010 when the difficulty was still very low you could manage pull it off but mining with these specs currently would be more a waste of computational power.

I think where you are actually getting it wrong is you are trying to compare your GPU capacity with those smaller ASIC mining wares in the market but they are very different. Your GPU is designed to carry out multiple tasks quickly but an ASIC ware on the other hand is designed to carry out a single task (hashing) very fast and efficiently and that's what mining actually needs.