It would if it has enough power. Current-drive amps are usually more suited to high-efficiency speaker systems. (Probably not Maggies.)
The main downside is.....speaker system impedance variations translate directly into amplitude response variations.
You pretty much need transducers designed for that type of amplifier. There are not many speakers that fit that category.
There are semantics involved here and not everyone's definition of a current-drive amplifier is the same.
Personally, I think power amplifiers should be voltage sources....not current sources.
Dave.