I don't see why not.
Your computer specs seems to fit the minimum system requirement for a Mac.
You probably want to turn all your graphics quality to the lowest if you're experiencing lagginess.
If you've never installed Starcraft 2 before, you'll likely need to download 7 to 20 GB of game contents. I hope you got unlimited internet download quota and a high speed internet.
Blizzard and a number of other game companies are moving to making games where the disc is just an installer and the game contents are downloaded from servers.
They don't seem to put the latest game content patches etc on the disc anymore.
Disc 2 of Starcraft 2 Legacy of the Void is completely empty when I put it into my DVD drive, no joke. It's a sad state for the gaming community. Not nice for those on slow, limited internet bandwidth plans.
Happy gaming anyhow :D