Both me and my brother have been wanting to try this game and i was thinking if it would be possible to just buy it on one of our accounts at first and have us both log in on the same account and play it together? Since the game is DRM free this should be okay to do right?

This may work, but I doubt it would be consistent with the license terms. Most games specifically state one license = one install. Some structure it as one license = one concurrent use, so you would be licensed install it in both places, but not play more than one install at a time.

If you are doing this as a try-before-buy scenario, and intend to buy a second copy if you like how the multiplayer works, that would still probably be inconsistent with the license, but I doubt you would get much trouble for doing that.

to answer your question, yes it should work... assuming you have a network set up correct