Not really, but still kind of.

Image stabilization as implemented in lenses and cameras usually give you a relative (and not absolute) improvement over exposures done without image stabilization. Since the susceptibility to vibration or motion blur depends on the lens' angle of view, which again depends on the sensor size, and the absolute capabilities achievable with image stabilization depends on what you could achieve without image stabilization, sensor size is something you may have to consider.

I am not even sure if I understood my own explanation, so I'll try to give an example.

A common rule of thumb for hand-held photography is that you should use shutter speeds shorter than the reciprocity of the (35mm equivalent) focal length of your lens. E.g. when shooting with a 400mm tele lens, you should use shutter speeds 1/400s and shorter. This of course varies a lot from person to person, but it is at least a rule of thumb to start with. If this lens had image stabilization with an improvement of two stops, you would now be able to shoot hand-held at 1/100s.

If you use the same lens on a camera with an APS-C sensor with a crop factor of about 1.5, the lens' angle of view would be narrower, more precisely equivalent to a 600mm lens on a full frame camera. This also means, that you without image stabilization would have to use a short exposure time of 1/600s to avoid problems with vibrations. Even if the image stabilization still gives you a two stop improvement, with image stabilization you would have to shoot at 1/150s or less.

So yes, the sensor size is relevant. It does not have direct impact on the image stabilization itself, but changes the 'base line' of what you have to work with before considering the improvements gained by image stabilization.