If you intend to feed via the same jack as the guitar signal, you might need an impedance matching transformer in the gas can as well, i suspect like others that feedback might be the major obstacle though.
I think Sikes you are going to have to experiment. Never thought of , Paul's tin can idea it may work. Is it not just a peizo in a Tin can ? Have to agree with Darryl as well, if the mic is low impedance you will need an impedance matching transformer.
I am trying to understand the question a little better. You have a mic that runs on DC voltage and you want to power it with a 9V battery? It is sort of like Phantom power and that is what you would want to emulate. Crazy old guitarists used to power onboard electronics with 3 wire cables to get the job done. With 3 wires you can combine the audio signal ground with the negative side of the battery signal on one wire. Positive audio signal on one wire and positive 9V on the other wire. So you want the mic audio coming out of the guitar amp?I'm sure this has been done both ways. What you want to do can be done, but it does need to be done right. The input of your guitar amp does not want to see 9VDC , but you can block that with a diode. Let me doodle a little with a wiring diagram. It sure sounds do-able.
have you considered a ghs soundhole mic.. ? I love them.. they can feedback but only if you're close to the amp.. they require a AA battery.. they are a pain on a regular acoustic because of the battery location but on a gas can... or CGB .. you should be abe to design with easy access. and yes you can sing into it.. I used to sing into the soundhole of the guitar for fun..