No they don’t take regular soap.
They take a much thinner version of soap so at the very least you would have to take regular soap and experiment to figure out how much to dilute it by and then dilute it before putting it in the foaming dispenser. That’s even more work and potentially messier than just refilling it more often with regular soap.

Yeah my SO and I go through those little bottles. She washes her hands obsessively but even when it was just me, I basically never want to have to refill it. It doesn’t help that we have four different soap dispensers throughout the house at different sinks and for different purposes so it feels like one of them always needs to be refilled.