Yes, the C7200s support online insertion and removal (OIR) of port adapters that are of the same type (ie., same part/model number). I have done this on several occassions on C7206VXR routers without any issues. I've had luck inserting a new port adapter with power to the chassis as well. However, this requires a reload for the proper microcode to be loaded to support the interface.
You should also be aware that the 7206 chassis has a split mid-plane requiring certain considerations when installing additional interface hardware. There's plenty of documentation on the Cisco website...an excellent tool!
Regards
