J Pickup Wiring Kit for PJ Bass

You can, but I recommend two things:

Make sure it has 500K Ohm pots.

Don't get one that has those gigantic capacitors.

This is an example of an over-spec'd capacitor:



in a bass or guitar, we are dealing with less than 1 Volt of output, so we don't need capacitors that are rated for 600 Volts

Here's a drawing to compare prospective "harness" candidates with:

https://www.seymourduncan.com/wp-content/uploads/2016/05/P_JBass_Standard.pdf

The representation of the capacitor is about right as well. It doesn't need to be bigger than a Chicklet:



My advice is really to buy the pots & wire & do it yourself. You can probably re-use the capacitor you already have.