I've been playing ABG's for years, and DB for 8 years before that. Like everyone says, they do not look, play or sound the same. Which is why I used both at my last acoustic set. There is nothing, absolutely nothing like the look, feel and sound of real DB on stage. But it's so much easier to play diads, triads, and upper register fills on an ABG.
My ABG is a Spector Timbre, strung with flats. It sounds a bit more thumpy and airy than a P-bass but otherwise it's still a BG. However, it looks the part, and for most audiences that is enough.
I also have a Yamaha BEX-4, which is a thinline bass with both mag and piezo pickups. While it has a neat sound, it's also not the sound of the DB. But it has that hollowbody look, and the audience probably won't know the difference.
And I have a MIM Fender Power Jazz Bass, which has the same Fishman piezo bridge and preamp as the Spector Core. Mine has been customized with a fretless neck, and with flats and the right technique it does an admirable job of sounding something related to a DB. But of course it still looks like a J when you're on stage.
So, to the OP and anyone else in a similar situation:
If you're just going for the look, this is a good excuse to invest in an f-hole hollowbody.
If this is simply justification to buy that Taylor GS Mini or other short scale ABG you've been eyeing, do it.
If you want to experiment with tapewounds and upright techniques on your fretless, that answer is always yes.