There used to be a Pro Tour player who played that way and annoyed the hell out of his opponents. If you can reliably play like that, I think it's awesome because it distracts opponents like nothing else.
If my opponent were quickly shuffling his cards around in his hand, I might take it as a tell.
Didn't we already establish that there is a major difference between actually shuffling the cards and just moving them around in your hand? For example, many players have this "two card vs two card" move, taking two cards not adjacent and moving them to a different place when contemplating a play. (I can't describe it accurately, but I think you've all seen it before.) That's mostly automatic, and not a problem at all. If you keep your cards still, sure, go ahead. I don't, and I don't think one is worse or better than the other.
Only if I had an opponent who puts his cards like Buttons does, I'd probably ask him about his morphs all the time.
Would attractive members of the opposite sex think I look stupid doing this, and if yes, is it really worth it?
You play Magic: The Gathering -- so yes, and yes.
Dozer