Not uncommon at all in the US in "upstairs/downstairs" FAA facilities. Sometimes the TRACON is open, and other times radar is combined at the local control position, depending upon traffic/shift/etc. I always felt the worst part of this arrangement was loss of the BRITE for the close-in guys. When you crank the BRITE out to 60 miles to run approaches, the display provides no help at all for the pattern.
As for Kwaj... When last I saw that operation it was run off of separate displays (enroute and tracon) and the displays themselves didn't inspire me. That two-scope methodolgy is bad enough in a reguar CERAP. To toss tower into the mix is, in my opinion, a bit much, even if it is with the kinds of traffic counts and predictable movements Kwaj enjoys...
I note that, from a mil tower/TRACON controller standpoint (LONG time ago!) lack of atc staffing wouldn't be problematic shoud an attack come to pass on a Sunday. In my experience, those boys and girls in the g-suits are going to depart and go where they go, regardless of your level of cooperation in the tower...