While this is an interesting question, I'll have to make the killjoy here and say, No, this is quite unlikely (even if I don't have a hard proof either and interpretation is still a free good).
First of all, as Oliver_C points out in his comment, it is not entirely clear if Heath Ledger commited suicide in the first place and the official version is that he didn't.
But even if he did then this suicide note connection can only be unintentional, since he was not so much responsible for the story and making of the movie at all, he just starred in it. And it would be extremely unlikely for him to have some weird arrangement with Terry Gilliam to make him some kind of "suicide note movie" for a long planned suicide. Likewise his death was initially a pretty severe problem for the yet unfinished movie (before they came up with the genuine idea of replacing him with other famous actors in the dream world):
Gilliam was presiding over concept art when he was informed by a phone
call that Ledger had died. His initial thought about the production
was: "The film's over, it's as simple as that."
So it seems pretty unlikely that Heath Ledger planned his suicide (if even suicide at all) such a long time in advance and managed Terry Gilliam to make him a personal suicide note movie.
And furthermore, he was quite different from his role in the end:
To escape the "dream" which he was in, he had to kill himself to be
the last person they needed to save Parnassus's daughter
While this is true, Tony (Ledger's character) certainly did not want to sacrifice himself but, as we learn during the movie, always had quite selfish intentions. He needed to be tricked into death by Parnassus (who offered him a fake pipe that didn't help him survive at the gallows). So even if by actions, Tony did not commit suicide by intentions.
So all in all I think your theory doesn't hold water and I guess you might be able to interpret something like this into any of Heath Ledger's later performances if you really want.