The e6300 means you have one of Intel's express chipsets (945, G3x, G4x). The onboard gpu on these isn't something to sing home about.
But even before we start thinking about any of the questions you have asked, it would be useful if you could specify the Manufacturer/Model/Chipset of the motherboard.
Whether you can add a dedicated GPU depends upon whether your motherboard even supports one. There are intel implementations of G31 (Most rampantly sold in India) which does not have a PCI-e slot at all. If you dont know the exact model take a picture of the innards of the case showing the mother-board, it should give a clear idea.
A current generation GPU which would run fine without your e6300 being a bottleneck like the AMD 6750/6770 would hardly be bothered by heat or dust. However, it is always advisable to have a case big enough to accommodate the card so that it could breath (decent airflow).
Another issue you may face (Going by my experience in India) is you may have a stock PSU bundled with your cabinet. Which would certainly be the biggest thorn.
Now to answer your first question, No it wont consume more CPU cycles, than your onboard implementation.