Is it fine to connect a power strip with A/V to one input of the power conditioner?

You can use a power strip connected to your Shunyata PC. I am doing just that for the powered woofers in my Golden Ear Triton Reference speakers. I have a Hydra 4 with one speaker plugged directly into it. I am using a power strip plugged into the Hydra for the other speaker because the high end PC I am using wasn’t long enough. No difference in sound and Gabrial or is it Caleb at Shunyata told me this when I called to inquire. It has been this way for 7 years. I also charge my iPhone & my iPad onn that strip at the same time (2 wall warts) while the system is playing with no ill effects at all and no noise when plugging and unplugging the devices.

Yes, there will be no interference from the other components. I use 3 Shunyata Hydras in my main system.  One Hydra has a home made power cord which goes to my TV where I use a Blu Ray player.  The rest of my TV setup goes to a Audioquest Niagara 1200 and is plugged into a wall outlet with the overhead lights on the circuit.  My Technics SL1200G  is also plugged into the Hydra that is used for the Blu Ray.  Shunyata told me on the phone I could do just that.  That is right from the manufacturers mouth to you.