In my opinion they're testing humanity, not XCOM. Once XCOM starts confounding them, the terror missions start, and they're constantly trying to subvert the XCOM project's government support. Doesn't make much sense if they're relying on XCOM specifically to create a volunteer.
And eventually they assault XCOM headquarters directly attempting to destroy it. To do so they practically ruin four psionic humans they engineered, themselves, without any reliance on XCOM. Clearly their abduction and experimentation programs were working so well that they thought they could afford to sacrifice these specimens - humans who exhibited psi powers well beyond anything XCOM ever discovers. And yet they were expendable, if it meant ending the primary source of human resistance.
I don't think the Volunteer was supposed to come from XCOM. The aliens do their best to erode XCOM's support, pursue their own highly successful research, try to wipe out XCOM directly at high cost, then do their best to kill the Volunteer *on the temple ship*. I think the closest this gets to being their plan is them thinking "Well, I guess our only chance now is to tempt XCOM's volunteer and hope it defects. Otherwise it'll probably kill us. Throw everything at them anyway, just in case... Call it a test."
Hm, I still think EXALT was working on a volunteer. They were certainly after Annette. Maybe the canon result is that EXALT, surviving like cockroaches, was able to train their own Volunteer who cooperated with the aliens.
Or heck, maybe the aliens did just build their own. I'd rather it be EXALT, though. Or have a rejected EXALT Volunteer be an important part of the story.