I am not a behaviorist, but i'd say if his anxiety is caused by or related to a bitch in season (somewhere with in MILES of your home), I'd say YES. If it were fall when the basenjis (boys and girls) are ususally in season, i'd say probably. Otherwise, it's harder to guess. Have you tried a DAP? I'd try that first. (DAP is available several places; try your favorite dog supply website or amazon and compare prices)
Is he calm when your home and anxious when you leave or go through the motions of leaving? If that's it, sounds more like separation anxiety and I'll look around for Patricia McConnell's booklet on that (try dogwise dot com)
I will look into the DAP. He is anxious when I am leaving. He gets a ton of energy and usually tries to grab me with his teeth when I'm leaving. Very playful like, but I can tell he is anxious.
When I get home he is very calm. But the behavior I noticed in the last few weeks is that he greets me when i'm home. Already in the Foyer. Normally he's relaxing in the living room and waiting for me to come to him (Gotta love these dogs). So I would strongly correlate the Foyer greetings with the destruction. That's usually the sign that he did some damage that afternoon.