Using an OTG cable while charging
Yes, it is possible, at least technically.  What you need is a cable called a OTG host cable with power, which is a double-female cable with a male micro, a female micro (which only has the power and ground connected, no data), and a female A, like this one.
Additionally, you also need software support.  I know an appropriate kernel patch is available for CM10 on the Nexus 7 (here), but I don't know about any other devices.