I'm pretty sure the whole point of the Unseelie Fey template is that they aren't pure-blooded fey, and thus the only way this idea would work is if you applied Unseelie Fey to a creature that was already a pure-blooded fey.

As long as you apply this process to something like a killoren (assuming they are written as being pure fey, which I haven't checked), you would indeed end up with a Seelie Unseelie Fey by RAW, but it's not exactly a revelation that a pure-blooded fey with no source of non-fey heritage is eligible for templates that apply only to pure-blooded fey.