USB to power other devices

Similar to @Jared's (admittedly "cooler" answer) you can buy a simple USB wall charger for a few dollars. They are cheap, and simple. Or, you might do like this guy's Instructable and DIY your own.

This doesn't in any way actually answer your question of how to make your PC shut down after the phone is finished charging via its USB cable, but it does seem rather superfluous to run an entire PC just to charge the phone via the 5V line on its USB hub. :)

USB devices start out as "low powered" (drawing a maximum of one unit load of power, which is 100 mA in USB 2.0, see 7.2.1 Classes of Devices, page 171), and can negotiate "high power" mode in which the device can draw up to 500 mA in plain USB 2.0. At USB's 5 V DC, 500 mA provides 2.5 W of power, plus or minus tolerances.

The operative word here is negotiate. The host is fully within its rights to refuse a USB device switching to high power mode if such amounts of power are not available for any reason, and the device must deal gracefully with failure to switch to high power mode. Likely, it will appear as though it is shut down if the negotiation to high power fails, or in the case of a backlit keyboard the keyboard might work but the backlight might remain turned off if sufficient power for that feature is not available.

As has been pointed out by arch-abit, the power consumption of the keyboard (or even the keyboard and mouse combined) is likely to be significantly lower than the 2.5 W allowed for by USB. Based on Journeyman Geek's back-of-the-envelope calculations in another answer to this question, depending on the specific LEDs used and their light output, it might quite possibly fit well inside the 0.5 W (100 mA) allowed for by the initial low power mode. LEDs are very power-efficient; a few watts into a LED lightbulb is enough to provide general lighting for a small room, so a keyboard certainly shouldn't need more than a few hundred milliwatts (a few tenths of a watt) for its background illumination, and quite possibly significantly less than that. After all, we are talking about background illumination to help you see the letters printed on the keys in otherwise dark conditions, not general illumination.

If all devices involved are USB 2.0 certified and can be used without weird constructs like USB Y cables for power, you likely don't need to worry at all. If the switch has an external power supply (functions as a powered USB hub) then you almost certainly don't need to worry. The worst that is likely to happen is that something won't function, or will function only erratically (depending on the instantaneous power-up ordering, for example).