Should I run leads from my amp to the sub, at the same time as running speaker cables from my amp to my speakers?
Yes. The input impedance of the speaker-level inputs of the sub will be very high. Therefore it will present a negligible load to the amp, and the wiring between the amp's output terminals and the sub doesn't have to be heavy gauge speaker wire; much narrower gauges will work fine for the sub connection too, as long as the main speakers are connected directly to the amp with heavy gauge cable.
REL subs, for example, come with a narrow gauge 3-wire cable which can be used for that purpose, one wire going to the left channel + output of the amp, one wire going to the right channel + output of the amp, and one wire going to the - output of either channel. (Connecting to the - output of the other channel isn't necessary, as the two - outputs of an amp that does not have balanced outputs are presumably connected together within the amp).
Regards,
-- Al