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

Don’t plug your TV, wall warts, blue ray player, etc into your power conditioner. plug them into the wall, if you need a pwoer strip, plug it into the wall for these lofi accessories.

Keep wall warts away from everything else. Isolation is the key.

If I could plug my wall warts into one of my neighbours outlets, I would.

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.