You sure can. I do. Well i'm not sure about private servers but I assume you can run those too. Also, you can connect to a VPS/server for botting purposes also, just like you would do so on windows.
As kill dank said, it is a lot more annoying to bot on a mac. For example, to connect to my rsbots.net bot client every single time I want to open it I need to enter the following commands in to my terminal: