Yes. If we talk about an actor instead of an engineer, for example, then it does add to the meaning.
"I am an actor." Every waiter and bartender in Los Angeles is an actor.
"I am an actor by profession." Now, if he's telling the truth, then he makes a living with acting. He doesn't have to wait tables or tend bar.
In my personal understanding as a native English speaker, Vocation and Profession are identical words. I personally think the sentence is awkward with "by profession." I don't usually hear this expression. I hear "as a profession," maybe. I hear "professional" if it proceeds certain jobs/vocations/professions. But, I do believe the words are as perfect of synonyms as synonyms can be. ;-) Maybe I'm wrong, but I don't ever think of a calling that someone loves when I hear vocation. In fact, I never even connected the word with "vocative" or "voice" before this particular discussion. Hah. For me, it's just a word for a profession.