I don't know if they did a whole tour but Cardiacs certainly played at least one gig supporting Marillion at the height of the latter's mid-eighties pop success. I wasn't there but they apparently went down really badly. Story is that bottles etc. were thrown, much to the disgust of Fish who was a big fan and had personally requested them as a support act.
I can ask someone who was actually there if you want further clarification.