Short answer is don't MIG on a bicycle.

Long answer is it depends on the tubing. If the wall is thick enough then you should be fine, but typically good bicycles are made with very thin walls and few MIG machines have the control to avoid a bad overheating.

If you happen to own a Millermatic 350 then you might be OK but the 251 has problems and you better not be asking this question if all you have is the 135.

On the other hand, if you are making a chopper out of a few Huffys and some box tubing then go for it, there isn't enough stress to really cause a job like that to fail, and you should be only riding it at slow speeds in some sort of parade or something so if it fails you wont get run over.

Milo