if V=IR and we assume in our case that for the same picking force the V is constant then raising the R will result in lower I. That means weaker current hitting the amp. What is the result of weaker current through the amp?
sorry, thats an extremely gross simplification, and incorrect.
but even entertaining your suggestion - the effect is nothing. guitar amplifiers are voltage rather than current driven.
the guitar pickup is a highly non-ideal device, and has an impedance which is loaded by following components. if you increase the load on the pickup, with a lower load impedance (pedals, volume pot, tone pot, amp input) - then the voltage produced at the output of the pickup is lower.
but even this is too big a simplification - pickups are inductive and capacitive - the affect of loading will be different at different frequencies. its extremely difficult to model these. but essentially its the higher frequencies which are attenuated more.