As the title suggests, I've noticed battery was just OK, I'm guessing this is sapping all my battery, how do I get it to just come on when I unlock it?
I think if you turn off an option known as "Connected Standby" it will do that. Can't say for sure though, as my old laptop does that my default and I can't do anything about it.
I would poke into the power settings on the desktop.
It is by design. It is the same that other tablets like iPad, and most smarphones, do. This way they can get notifications and updates in real time. I don't know if there is an easy way to change this behavior on Surface (like there is on Windows Phone).
Given the size of the battery of a tablet (10-20 times bigger than a phone), leaving wifi "always on" is not such a big drain as you might think.