... the BN has sometimes been referred to as "a jazz bass on steroids". How well does it cop a P bass tone?
Theoretically speaking, Zortaion is right, but practically speaking it's not so black and white, simply because (as Richard_P_Harve and YCBass have inferred), there is more to shaping our tone than playing a bass at its default settings.
In my view, part of the answer to your question is embedded in the question itself.
As you said, BNs are wonderful sounding JAZZ basses. If you think a great jazz bass can produce an acceptable pbass tone for blues with with help from on board and amp tweaks, then it stands to reason that a BN will as well, and perhaps do it just a tad better.
I guess I'm one who thinks a Jazz bass can (with some help) do an acceptable blues pbass tone. Ed Friedland, the "bass whisperer," seems to think single coil Jazz bass pickups can approximate pbass tone in certain cases as well, as you can see in
this video clip bass review.
Ed refers to one j-style single coil tone as "a p-bass killer if I've ever heard one." Of course the placement of that pickup is part of the reason why.
I've read that both halves of a split P Bass pickup are wired in-phase, in series and are hum cancelling.
Of course, BN pickups can be set to be hum cancelling as well.
The in-phase series wiring of passive pickups tends to cut highs and accentuate lower mids, a tone very similar to an Fbass BN4 set in hum cancelling mode with the tone rolled back slightly, and bass and mids boosted a bit.
That said, I'm sure that experienced ears listening to a recording could tell the difference between a pbass and a BN, but these experienced ears would probably think the BN fits right in with that genre of music and sounds great.
Of course, probably the best thing would be for you to get down to that seller and give the bass a test drive yourself and see if it works for you.