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

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.

I'd generally avoid plugging a surge protector or power strip into a nice conditioner. This is for a couple reasons. First, there is a solid chance it will insert noise into your signal, but second the draw on that one outlet may end up being more than is intended. You're gonna want that power amp to have lots of current available and by sharing it's outlet with other items you may end up choking it a bit. I fact, there are those that done use conditioners for their amps at all because the circuitry tends to limit power a bit. Just my $.02

Great discussion.  I'm a newbie, so what's  a "wall wart" ?

@max_sansui 

A "wall wart" is a colloquial term for a small, external power adapter that plugs directly into a wall outlet, essentially a transformer box with a power cord that provides electricity to low-power devices like cell phone chargers, routers, or electric toothbrushes; the name "wart" is used because of its bulky, unsightly appearance protruding from the wall socket.