Is it possible to hook up a stock sub to a headunit other than Subaru's 6 disc changer?

 

Yes, the sub connects via a bridging harness that taps the rear speaker outputs. It will work with an aftermarket unit as long as it still has an internal amplifier, if you install a unit with no internal amp and line outputs only then it won't work.
I have an Alpine with the stock sub, it's been working fine for several years now.

Note- this should be the case for the 03 WRX as in your profile, the sub is the same as in my 02. More recent versions of the sub may be different and have additional connections into the factory HU so they may not work with aftermarket HU's.