Pickup has high mostly inductive impedance. So in first order modeling, lets swap p'up with 1st order equivalent circuit which would consist of voltage generator Vemf which represents total EMF induced in p'up, DC resistance of p'up Rdc, inductance L and series conection of pot nad cap across p'up R and C (which is tone control; I've ignored p'up equivalent internal capacitance to simplify equations).
Output would be:
Vout = Vemf * [(1+sRC)/(ssLC+s(R+Rdc)C+1)]
which is typical second order reponse.
When tone knob is fully open, R is 250K, and response is dominated by internal and cable capacitance Cint (not represented in equation above for reasons of clarity) with response 1/(ssLCint+sRdcCint+1). When you start to close tone knob, R drops and series RC conection start to dominate, with R reducing damping - incerasing Q of resonant circuit.
If you just put pot and cap in buffered box, it would act as simple first order RC which is not what passive p'up + tone control behave like (response would be (1+sRC)/(1+s(R+Rout)C) where Rout is output impedance of whatever is driving tone circuit). So you must put something that would simulate p'up impedance.
One more thing, that simple RLC representation of p'up impedance is simplest model, because of nature of pickups closer model would be of considerably higher order. So closest aproach would be to put some actual cheap p'up in pedal.
further reading:
Magnetic pickups Pickup emulation RC circuit RLC circuit
