I've used aerobars a few times on our Co-Motion Speedster, partly for comfort on long rides and partly for aerodynamics. The tandem feels even more stable when on them than on aerobars on my single bike. I'll happily stay on them until about 50 kph (30 mph) or until we come up to traffic or an intersection, when I move my hands to the controls.

For aerobars that you're clipping onto regular drop bars, try to get some that put the pads directly on top of the bars, with the extensions supported either below or inline with the regular bars; I've used some that put the aerobars on top of the drop bars and then the elbow pads on top of that, which is just way too high. My personal current favorite clip-on aerobars are those made by 3T, they have an aluminum and carbon model, but when buying them be careful because the extensions are sold separately from the supports (which allows you to choose the shape of your extensions).