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

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. :)

@erik_squires that was my other option. Wondering if the blue ray disc player could be within the hi-fi grouping. 

I'd try it. :)  The real issue is how much noise the power supply puts out.

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.