It's never done it on my SP3, nor did it on my SP2, but it did with my SRT.
The explanation I got for the SP2 was that when it is in standby, there are NO parts in an ON state to be able to detect the cover being opened, as keeping something in an ON state would drain battery.
This was the opposite with the Surface RT, which was in a constant connected standby mode, therefore the necessary hardware to detect the keyboard being opened was on and could wake the device.
Now, SP3 - that's a bit confusing. As has been said, for the first 3 hours I believe it will stay in the Connected Stand (now renamed InstantGO) which I would assume would allow it to be woke by opening the cover (like the RT), however I have not seen this on mine.
Whether it is supposed to? I guess asking Microsoft would be best.