Not all the time.
CFL type bulbs; unless sold as dimmable; should not be used with a Lamp Module. Dimmables; vary by brand; on things like smoothness of dim.
Appliance Modules should run any type bulb; but the Local Control Circuit in them; make some flicker and turn back on. There are workarounds for this.
Two wire wall switches that steal power through the load will not work with a CFL; dimmable or not. Three wire ones with a neural connection manytimes work fine.
LED types in my tests stay on at about half brightness when off.
