Im just paranoid about dirt and what not getting in there. Just feels odd leaving off battery cover. I'm sure it'll be fine though
For the sake of peace of mind, you may be better off just ordering yourself the extended Surface case. Recently, I had a change of events that necessitated me having to use my extended battery door on my case set up.
As explained on a Ghost Armor thread, my Otterbox Commuter case (which by my personal preference, was used without my extended battery door cover) was causing certain edges of my Ghost Armor screen protector to get pinched and subsequently come off the screen.
It would appear that the pressure caused by the lower part of the phone's case, when being inserted into the hard holster, would push the silicone liner's edge into the Ghost Armor.
As a result, I installed the extended battery door, reinstalled the Otterbox Commuter, and it hasn't interfered with my screen protector yet. The added material of the door reduced the amount of pressure flex in the case and allowed the two to play nicely.
Again, I don't think you would have any issues with using the Seidio Surface without the door, but if it really bothers you, consider the extended version.