Rationale for what I'm trying to do: I'm trying to update my house to use "smart" lighting and one device I want to update is a smart lamp in this style but with replaceable bulbs. If I switch over all of the bulbs to smart bulbs, then I'll be out a lot of money. I also fear some sort of dangerous consequence to there being a leading edge dimmer on the lamp, so I'm avoiding plugging smart bulbs into it.
Given the above rationale, I'm wondering if I plug the lamp into a "dimmer plug" such as this one if there will be any severe consequences due to the fact that there is a dimmer switch on the lamp as well. The dimmer switch on the lamp is likely of the leading-edge variety, as it came with incandescent bulbs. I will also plan to use LED bulbs in the lamp and keep the lamp's dimmer slider to its highest setting and only use the smart dimmer plug for controlling the light.