Yes you can run both the 802.11a and 802.11b radios at the same time in a AP1200 chassis.
There are limitations on using inline power due to the power draw but these are clearly described in the release notes.
The 2 radios will run as 2 seperate radio networks but both will share the common ethernet interface.
The 802.11a and 802.11b client cards are differerent so they will NOT interoperate ( that feature will come in the 802.11g standard) but you can use the dual band function of the AP1200 to have both on your network at once.
It should be noted that you can also order the AP1200 with both radios already installed, please check the hardware configurator for more details when you order these.
Here is the data sheet that will answer most of your questions
http://www.cisco.com/en/US/products/hw/wireless/ps430/products_data_sheet09186a00800937a6.html
David