'I invited' would indicate you are now at the party talking about an invitation in the past.
However, the question states 'I've invited' which would mean before the party which would necessitate the use of 'He'll come' because it's referring to the future and there's doubt involved.
Am I the only one that doesn't like "doubt if"? I'm sure I always say "doubt that".
[edit: Just out of curiosity, I did a Google search, which turned up 3 million+ doubt ifand 53 million+ doubt that. But of course that doesn't take into account the rest of the context which could make a difference.]