This is more of an English question: Could you say "I am your boss to be"?
Yes. It's a bit more poetic sounding then just "I'm your future boss", but it's correct English.
I wrote "I am about to become your boss" and it's wrong. Is it really wrong or could you count it as a wider translation?
I would understand you perfectly. The fact that you used "about to be" suggests to me that it might be just a bit more imminent than "future". Maybe someone with more knowledge of the Swedish language than I have could translate your sentence to Swedish if the meaning is a bit different than "I am your future boss"
Is there a sense, in the Swedish sentence, that there is a meaning that would be different from saying in English that "In the future, I will be your boss"?
Not that I can think of, no. I mean, sure - there's the obvious grammatical difference in aspect, but that ought to have little impact in practice. They do mean the same thing.
This suggests to me that the "blivande chef' is going to be joining the company or department, rather than someone already there who is being promoted and now fills the role of my 'boss-to-be.
"I am your incoming boss" also sounds a little too formal and perhaps directive to me--if the supervisor wants to begin in a friendly, easier way, but that's just my take on it. ;-)
Would adding this comma change the meaning in the same way in both languages?
"I am your future, boss." "Jag är din blivande, chef."
Or maybe that doesn't scan in Swedish, and you'd have to use "framtid"?