Sure you can! Just, probably not very well on PC. You can pretty much forget about graphics card acceleration. To quote Patrick Hughes' answer to another question:
[PC is like the] wild west, barroom brawls and your OS is the sheriff keeping everyone from getting shot.
[...]on home PCs you have to support tens of different chipsets that have to work flawlessly against millions of programs written across the past decade or more? Personally I think that it's a miracle that the house of cards keeps standing!
As a business venture there's just too much going on there for you to be able to confidently support much more than your own PC, let alone the variety of quirks that crop up on other people's systems. But, if you're just interested in learning things about low level tricks (which in today's world only come up if you're working on drivers/middleware/APIs - things studios don't really do) and thus don't care too much about compatibility check out some of the code released from demoscenes, at ie
The Great Demoscene Sourcecode Giveaway.
Or, as a technical exercise, writing a game from the ground up targeting a simple platform like Arduino is completely achievable. Since it's essentially just a flashable chip, you'll have to decide on the parameters of your game. Maybe you skip the screen and do sound only? Strange controller? It would be a good setup for getting into console development.