I've never painted speakers, but back in '02 I was working in a composite shop and I brought in some wooden window shutters, sanded off the old finish, shot them with two coats of USAirways blue and then a coat of clear and they are still holding a gloss shine to this day, so I do not see why it could not be done with wooden speaker cabinets. .
Are the speaker cabinets actually made of wood? I've sanded some stuff before that wasn't wood, and some of it does some goofy stuff after the paint comes off. I have no idea what it will take to get that gloss white to start coming off . . . maybe just start with a small inconspicuous area with some 80 grit (or even 100 grit) and see how it goes before you start sanding a large area.