Bass guitar is all about tone. Not a day goes by here without someone talking about tone. Whether you like the P bass, Ric, Stingray tone, etc...it's not just the pickup(s) but the on-board controls, the strings and the amp. Earthwood bass, jumbo-body Guild, Taylor AB-3, no matter what acoustic bass you use, you're limited to that basic tone.
I have a great acoustic bass but I wouldn't dream of playing unplugged and limiting what it can do, and believe me, I can get some sounds out of it that I can't even get out of my G&L L2000...that's why I bought a battery-powered amp.
Sure, you can be heard on your Warwick Alien, to some degree, when playing with an acoustic guitar or two, but the bass won't be fully realized when the tone is restricted.