For your original questions, you cannot at present get SmartThings to recognize the Pico remote in any fashion. However, if you also use the Staples Connect, you can create parallel control paths so that the Pico can turn off a zwave light that is also controllable through SmartThings. It’s very important that you not read too much into that–a lot of the controls are one way and statuses are not necessarily updated. Note that the Pico is communicating ONLY with the Staples unit, so it can only control devices that are paired with it. Which means no virtual switches, no mode changes, etc. And it doesn’t give SmartThings control of the Lutron devices that are connected to Staples.
@KingPumpkin is a community member who has both Staples Connect and SmartThings and has used the Staples Connect as a secondary zwave controller to SmartThings. See: