Couldn’t get an answer with Google. Right now I have a smart bulb that obviously disconnects from ST when I switch the switch off. I instead want the switch keep a connection even when I turn it off. Will a Lutron Caseta switch connected to its hub, connected to ST keep it on so that I can control it anytime with my phone as well as the switch?
No. The Caseta switches work essentially like any other regular switch and will remove power from load when switched off. I’m sure others like @JDRoberts will give you some ideas about how you can achieve what you want, but generally it isn’t a good idea to use a smart bulb with a smart switch.
I have a few rooms in my house where the light switch controls one half of an outlet for a lamp. What I did was rewire the outlet so that both plugs are hot, then replaced the switch with a smart switch. I use the smart lighting app to turn the new smart bulb on and off when the switch is turned on and off.
It’s not about using both at the same time. Rather it’s that a smart Bulb should always have current running to it. It’s all right if there is occasionally a power outage, but if you are regularly using a switch of any type, either dumb or smart, to completely cut power to the bulb, the inrush current when power is restored can damage the radio over time, making your expensive smart bulbs that much more expensive as their life can be significantly shortened.
This is why the user’s guide for all the smart bulbs will tell you to leave them on power.
Fortunately, as I mentioned, there are a number of ways around this issue which will give you a natural switch on the wall while not damaging the bulb over time.