Well, I plugged it in, and the difference in sustain between the E and the other strings is still noticeable.
Here's a clip of me playing four notes on each string starting from E, trying not to change the touch:
https://soundcloud.com/easylungs/ubass-e-string-sustain
Here's another clip that is more musical:
https://soundcloud.com/easylungs/kala-ubass-fretless-mahogany
(Setup: UBass -> Boss RC-300 Looper -> line input of 15W Crate bass combo; the instrument input doesn't work; recorded from the laptop mic)
While in the latter setting the difference is less prominent, it is still noticeable. I cannot attribute it to the pickup because I clearly hear and feel it unplugged. I restrung the E, but nothing changed. Maybe, just maybe the string can vibrate more freely if I raise its nut slot a little bit with something like epoxy. Also, if it's possible at all to raise the bridge saddle without degrading the acoustic coupling to the pickup, I'd like to try that, I just don't know how yet.
Well, I guess I can adjust my playing and bass parts taking this into account. The instrument is otherwise incredibly cool. I also will try other string types.