I've shot some long exposure scenes that were absolutely ruined by having IS turned on with my 70-200 2.8L IS II lens . I wouldn't trust it at all, even if it claims to have tripod detection.
The effect must be different with video vs photo. I've filmed a lot on a tripod with that lens, and never saw a problem with the video. I have seen problems on long exposure photos though. And I've seen problems with the 24-105 when IS is on using a tripod. Also the 35 f/2 IS has never given me a problem with IS on.