Was the bass designed to be used with or without amplification? In the studio, do you mic the instrument or the amp? Some basses blur the line (ABG's), but for the most part, they're easy enough to classify.
It all starts with vibration: plucking the string. The harmonics of that oscillating string are determined by the bass' mechanical properties. The vibration of that entity creates the sound. But the pickups sense oscillation, so the sound is simply an artifact. If it was useful, we'd be mic'ing our EBG's in the studio, not plugging them in.
My definitions: sound is what you hear when playing unplugged. Tone comes from the pickups.
Does the sound of an EBG reflect its tone? Sometimes... to a limited extent. Frankly IMO, all EBG's, even the highest-dollar ones played by the highest-caliber players, sound like crap unplugged: too much treble, not enough bass. But even when accounting for that, I've heard basses that sounded reasonably good when unplugged but had poor tone when amplified, and vice versa: poor sound, great tone.
Another tack: A Sadowsky J-bass can be ordered with JJ pickups, PJ pickups, and the "reverse" PJ setup. The bass will
sound the same regardless of which pickups are installed... but these pickup configs produce different tone. No matter how transparent a pickup is, if you change its location and/or aperture, you get a very different tone from the instrument... dynamics, too. Jaco couldn't work his magic to the same extent on a stock 1957 P-bass (try squeezing burps or harmonics out of that)... but add a J bridge pup to it, wahlah... he can pretty much do his thing. Still *sounds* the same unplugged, just has another pickup for different tone and dynamics when amplified.
Point being, I see no disconnect. To the contrary: if you disconnect the pickups from an EBG, it's nearly useless. With DB, not so. Therefore an EBG is an EBG... nothing more.
P.S. I realize this is a semantic argument (an entertaining one for me, obviously

). I completely disagree with acoustic elitists who say "you can put strings and a pickup on any old plank of wood and have yourself a fine EBG". But I also disagree that a solidbody bass can be classified as acoustic simply because it produces some sound. That sound is never used for makin' music.