From experience, adding a capacitor to a bridge pickup won't make it sound like a Rickenbacker, nor will it particularly change how the pickups interact with each other.
A Rickenbacker pickup sounds like that regardless of the cap, that just changes the character slightly.
I added a cap to the back pickup on a BC Rich and it certainly thins the tone out... at the moment it's got a push/pull for series/parallel output from the pickup but I might change this to switch the cap in and out instead.
On a Rick, when both pickups are full on with the cap engaged they interact very differently, resulting in a less scooped, hollow twang like you'd get with a Jazz, for example.
On my BC Rich it still has that hollow twang to the top end but still retains the mids, if that makes sense.
By all means try it, you might have more luck than I did!
Picture for no reason other than it's a cool looking bass!