Could be, Geekboy. I didn't see any overt unhappiness in Johnny. But I was always struck by his saying, "I'd do anything for my Godfather," and not, "I'd do anything for you (emphasis added). In the novel, in an earlier setting, Tom visits Johnny in Hollywood to tell him that Vito will help him get an Oscar, and will help arrange financing for a movie Johnny wants to produce. Johnny asks if he'll have to do favors in return, and Tom says of course he will. "The Godfather has to ask me himself," Johnny replies. "I won't do it if you or Sonny ask.".
IMHO,when Johnny said that to Tom,he was doing it more to prop up his self-perceived sense of ego by suggesting that he would only answer to Vito.
In reality,after seeing first hand what the Family was capable of (the bandleader, Woltz,etc) Johnny had to know that he was nothing more than a common minstrel,bought,paid for,and owned by the Corleone's.
I would love to hear him refuse a favor that Tom asked . "No problem Johnny,if you don't want to do it,fine.I gotta get back to New York now.I promised your Godfather I'd keep him informed. What's that? You changed your mind? Ahh Johnny that is most appreciated.I see why he loves you so much"
