Hmmm, I have all three (LHT, clickstand, and a BOB), but I haven't put them together (with the BOB). I did have the double kickstand and the BOB with my Raleigh on my last trip. I really had to be mindful about how I parked. My "rig" fell over several times. With the experience I have with the clickstand supporting my fully loaded LHT (panniers front and back with tent and sleeping bag on top of rear rack), I would be very surprised if the clickstand did not work in the scenario you describe. Make sure you buy the Tour/Tandem bike specific model.

My LHT is on the trainer right now, or I'd go out and fit it all together and give you a report.