I would expect a DSP speaker to play louder if you HP the input in almost any case. Even if you only limit at the input, your overall signal level is going to be lower after the highpass, meaning you can increase the gain and make the rest of the signal louder.
I am actually having trouble thinking of a scenario where you wouldn't get a net gain in the mids/highs this way... possibly if the bass is already heavily compressed / limited / filtered so a reasonable HP doesn't get you any headroom. Possibly if there is an overall SPL limiter that is (for some reason) already so low that bass output is already not a limiting factor. (would be very odd.) Basically, highpass should always give you a little extra gain as long as the speaker is well implemented. IMO...
I am actually having trouble thinking of a scenario where you wouldn't get a net gain in the mids/highs this way... possibly if the bass is already heavily compressed / limited / filtered so a reasonable HP doesn't get you any headroom. Possibly if there is an overall SPL limiter that is (for some reason) already so low that bass output is already not a limiting factor. (would be very odd.) Basically, highpass should always give you a little extra gain as long as the speaker is well implemented. IMO...