FWIW, the minor diplomacy is more of a EIH feature and many EIA vets don't care for it. But it's a non-optional feature in the game so players need to consider it.
I would recommend checking the Minor Country Chart (15.2) and seeing which MPs have historical influence (e.g., Turkey has +3 for Algeria). Also carefully review rules 6.1.2 and 6.1.3 for how Influenced and Allied minor countries are treated. The greatest advantage appears to be having an Allied minor before having war declared on you, and having that Allied minor in a position to help you in some way. If you lose the war and go into Instability or Fiasco you'll lose the minor anyway. So maybe a few $$ invested will help some, maybe not. A disadvantage of having an Influenced minor and having it attacked is that you take control but also that you lose PP when it gets conquered. If you get a lapse of war, you win control of the minor and the other guy loses PP, but otherwise you're spending $$ and risking a PP loss.
So is it worth it? Good question. I don't know. I find the minor diplomacy feature an interesting sideshow but not convinced it does much, either for good or harm. I would also be interested in hearing from others, particularly if they played EIH.
Empires in Arms Development Team