So far BATFE has tacitly allowed it. The official response (from BATFE, you can see the letter) was that it's not a fully automatic weapon because each discharge requires a separate action (forward pressure on the forward grip to return the weapon to it's initial state, combined with continued push backward on the trigger). Since technically, the system allows the trigger to be released after each discharge (by recoiling the weapon into the stock), each discharge is a separate trigger pull. Now, the end result is well within the letter of the law (hence the official response), I do not see it being very long (especially if it's popularity continues to rise) before a regulatory adjustment is made. Of course, such an adjustment is demonstrably litigable as the device fits within the current laws, and thus a de facto rule-based ban would be contrary to established law...such a rule could easily be held up by even a conservative court, if they were operating in any way on public-opinion based "common sense" and not a strict interpretive method.
That being said, a friend of mine has one, and it's pretty cool. I want one, even though it's ugly as sin.