There's certainly no flutter when it's locked!
When in the fully unlocked mode, the Tremolno actually puts little to no resistance on the trem system, assuming it's installed correctly of course. I expect that a guitar that had nice flutter before installing one would still have it afterwards. My experience with a Tremolno was not entirely positive in that I could seem to get the thing installed exactly right such that it would completely lock the bridge from moving. I understand that they've come out with a newer revision in the meantime that's supposed to work better, but I haven't had a chance to try that yet.
In my mind, there's really no substitute for a true fixed bridge if what you're playing calls for one.