Bit of a weird question, but here it goes. I have a Leviton Z-Wave switch (single pole) currently powering my living room ceiling fan lights. Works great, no issues. I’m going to be adding 2 canister (recessed) lights in my living room that I’ll wire up simply to draw power from the ceiling fan lights. So my Leviton switch will control both my ceiling fan lights and the new canister lights. Simple enough, right? But I’d like to put smart bulbs in the canister lights to be able to control them somewhat independently from the ceiling fan lights. Will that work? I’m thinking I’ll only be able to turn the canister bulbs on and off if the Leviton switch is on and in turn my ceiling fan lights are on. That is fine and really all I want to be able to do. Basically if my ceiling fan lights are on I want to be able to turn my new canister lights off or on. I can’t think of a scenario where I’d want the new canister lights on and my ceiling fan lights off, hence why I want to wire them up directly to the ceiling fan lights and not wire them to a separate switch to have total control over them. Hopefully that all makes sense!! I have MANY smart switches and smart bulbs throughout my house all integrated with Smartthings and Google Home. But nothing quite like the scenario I just laid out, so I’m not quite sure if what I’m thinking will work.
No
If you want to use smart bulbs, wire them to the line side of the switch, if you don’t have anywhere else to pull from. You should never run smart bulbs on a smart switch, even a dumb switch is only for the rare occasion that the bulbs need to be reset/reconnected with the hub.
Makes sense. I wasn’t really considering the fact that every time I turn my ceiling fan lights off I’d be cutting power to my smart bulbs, which by design, are meant to always be powered. I have 4 or so smart bulbs installed in various lamps and fixtures throughout my house, but the “dumb” switches they are on are always left on. The bulb is always powered that way and can be controlled as intended through Smartthings/Google Home, and they all work well. I’ll just pull power from my ceiling fan lights as originally panned, install standard bulbs and forgot about trying to get them to work independently from my ceiling fan lights. I do not want to have to install a separate switch to accomplish that. Having them powered by my existing Leviton switch in conjunction with my ceiling fan lights will be fine. But it was worth a try.
If you kill power to smart bulbs, they come back on when the power is back on.
Plus, if you ever wanted to dim your ceiling fan light, the smart bulbs would not be happy about the PWM dimmed power.
So I got my recessed lighting installed. The guy that was doing it pulled power from my ceiling fan lights. Simple enough. But at first he mistakenly pulled power from the ceiling fan and not the lights. I didn’t think anything of it at the time, and he switched it to pull power from the ceiling fan lights and all was good. But now it’s got me to thinking. The ceiling fan has 2 switches. One for the lights and one for the fan. Couldn’t I rewire the recessed lights at the ceiling fan to pull power from the ceiling fan and not the lights? Then I could install a smart switch for the ceiling fan and then have smart control of my new recessed lights independently from the ceiling fan lights. I can control the ceiling fan itself by using the pull cord, but I RARELY use my ceiling fan so it would stay off 99% of the time. Thoughts?
For others finding this thread because of the topic title, this is a very good question and a very commonly asked one. 
I don’t want to jump into the additional details of fan wiring except to say that a double tap fan switch like the newest GE or Homeseer fan control models can give you a single gang wall switch with load control of the fan speed and scene control (no current change, so the switch sends a message to the hub and the hub sends a message to the smart bulbs) which can be very effective for some households.
https://shop.homeseer.com/products/homeseer-hs-fc200-z-wave-plus-fan-controller
Alternatively, you could add the same kind of double tap switch option to the switch that just controls the lights so one tap turns on just the main lights, double tap turns on the smart lights, etc.
Of course you still have to have things wired so the smart bulbs always stay powered in either case and then the wiring can get trickier in the kind of situation you’ve described.
As for the more general question in the topic title, please read the community FAQ. It details the various issues and options. 
(this is a clickable link)
BTW, a very simple way to handle your particular setup would be to put smart bulbs in the fan kit as well, and then you could have any combination of lights bright at any time. 
Leave the lights on power at all times and replace the Leviton light Switch with one of the doubletap switches or one of the other options in the FAQ.
That way you don’t have to worry about any impact from the fan motor control, or the fact that you had the lights wired in sequence.