Not saying that it sounds like one one, only that this change moves it in that direction. My ATK had a particular character when I played it unplugged, so it's not just about a humbucker in the sweet spot.The tone is mainly pickup style/placement on an ATK/Stingray.
This high mass bridge hasn't completely transformed the sound, but it has changed it. Everything sounds a bit tighter/ more direct. Haven't decided if it's for me yet.
Just because it has the big shiny plate like an ATK, it's a stretch to say it now sounds like one. Especially when you haven't heard it!
This, to me at least, is a matter of subtleties. What I think of as a "modern P" (high-mass bridge, heavy, Duncan QP's or similar overwound pickups) is still recognizable as a P-bass when you play it. It doesn't sound like a Gibson, a Jazz bass, a Ric, or a Stingray.
But it has a more sculpted tone, longer sustain, and less character. The 60's Precisions and copies that I have really bonded with, all shared some common characteristics- light weight, original or at least vintage-wound pickups and bridge hardware, small frets, a wide fingerboard, shorter sustain, and a certain amount of uneven response that I had to play around.
They are flawed instruments to be sure, but the flaws are part of their character.
I'm not saying that my VMP5 belongs in that company (it's too mellow-sounding), but at least it's in that general "vintage" camp. And I'm definitely not saying that everyone should like that feel and sound- great records have been made with both types...