Didn't try it on the speakers.  Probably the only use people would have for this is if they find it difficult to hear stuff on the bus/train (though personally, the max volume on the PSP is already really loud for me, and I wouldn't risk damaging my ears like that).
Yes, it works with the headphones, and from what I can tell, it doesn't appear to be applying a gain, but it's so loud that I didn't turn it up all the way.