So, this is something I was a bit concerned with too. The drivers on the board appear to be limited to 500ma, and the servo outputs are limited to 25ma. The thing with the servo outputs is that they are switched inside the servo, so as long as the control signal is small, it's not going to mess anything up. The motors have a simple transistor driver, from what I can tell. (my eyes are going bad, so I'm not too keen on trying to read the SMD markings) That should be what you are concerned with.
Also, you want that current to be delivered from a separate power source. Read the instructions, ( I know! Such a strange concept!) In the back (Page 61 in my copy), there are projects to use motors and servo's. They give the current limits and tell how to connect a battery pack right before the servo project. I wish the motor project talked a bit more about the details on the board, and how it all works. Maybe refer you back to the page with the current limits and stuff. I don't know about every one else, but I normally just turn to the project I am interested in, and look there, and in the index for the info.
I wish there was more info on the board. I kind of want to mod it.
At $5 from Micro Center, this thing is becoming my go to audio hat...