You're gone, gone, gone

can have two meanings, you're right.  It can mean after you're dead OR after you've left me, so other lyrics will affect the meaning.

We don't use the phrase 'I'm gone' very often.  We use the past tense for example 'He's gone to the shops and hasn't returned yet'  but not really in the first person e.g. using 'I'.   In fact, to say 'I'm gone' , in England this actually means, 'I'm drunk' i.e. I have drunk too much.  But again, we don't really use it.  It is used more as a verb (to go) than as an adjective.  Thanks :)