I don't see how it could sound anything like a Rick given the fact that Ricks are all maple neck through basses, and Mustangs are bolt on maple necks with alder bodies. I believe body and neck construction have more to do with a basses sound than the pickups.
Pickup construction or pickup placement? I think sticking a pickup down at the 24th fret position, and then at the 3rd-fret harmonic equivalent position from the bridge give a Rick bass its unique tone. The slightly shorter scale than Fender also make the strings slightly less taught at equivalent pitch, which also adds to the unique tone.
Rickenbacker fans often seem to think that Rick bases conform to a completely different set of laws of physics... then again Rickenbacker fans are cagey about the wiring in Rick basses, as though caps and resistors act completely differently in a Rick instrument, and again don't follow the laws of physics.
I suggest that OP doesn't get their hopes up, and that Chris Squire tones will fall onto their lap. However I think they will be surprised at what happens when you put pickups in the classic Rick positions, and lose the typical Fender "sweet spot" placement.