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

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. 

@stereo5  thanks. In your case I wouldn’t have a doubt. My case is a bit different and wondering if I can plug tv, blue ray player, streamer and power amp on one power strip and plug that into one Hydra outlet. 

If the outlets in your Hydra are isolated it’s probably no problem and may be why Shunyata said it’s not a problem.  I’d check that for your specific model, but you can always just try it and see if it results in any degradation in 2-channel performance with the power strip plugged into the Hydra. 

My suggestion is to get a Furman PST-8 for all your non-essentials instead. Excellent surge protection and will keep the noisy appliances out of your cleaned zone.

While power conditioner quality may vary, it IS possible to inject new noise after the conditioner.  Wall warts, TV's, network gear, etc. should be outside of your boutique conditioner.  The Furman provides both excellent noise filtering and surge protection, not to mention convenience. :)