If you are in the US, the NEC prohibits it. Switches controlling receptacles must be rated for the capacity of the branch circuit. i.e. the breaker capacity. The Inovelli switches and dimmers are not rated at anywhere near 15A or 20A.
The reason for the code is that while you only intend upon plugging a lamp into the receptacle, there is nothing to prevent someone from plugging in a vacuum cleaner, for example.
What you can do with an Inovelli is to mate it with a dry contact relay rated appropriately in the receptacle box. Ensure the receptacle is fully powered. (It may be already depending on whether or not it is split.) Power the relay and use it to switch the receptacle. Then use the Inovelli to send scene commands to turn the relay on and off.
Alternatively, swap out the receptacle for a smart outlet. If the protocol matches the switch, you can bind or associate it. Otherwise, control it with scene commands.
See here for further discussion: