I have a fire also that has a pot, we have had birds fall down into the chimney and drop down into the back of the gas fire (behind the open fire back). Because of the warm decomposition happens quick, it won't be the smell that alerts you, it will be the hordes of flys that come after. I've had so many birds down my chimney and I'm sorry to say it but I've never had one survive :( You will know if it's dead because believe me if you don't get any smell you will get millions of flies. The only good thing is that they usually come out of the chimney to just die. Last time I had a dead bird up my chimney I had to contaminate the entire room with fly spray and condemn it for 3 days before going in with a hoover and clearing up the dead bodies. Sorry I couldn't give you any good news asza, unfortuanatly your chances are not looking good.
Dizmo.