I believe that this is exactly the artist he is referring to, and the meaning of the phrase is to essentially say that being painted by Sargent is something that should be done in one's lifetime, with the mention of going to heaven being used as an allusion to dying. So if you die before you get your portrait painted by Sargent, you died too early.
Imagine a similar phrase of "If you die before you go to Disney World, you died too early."