Not that I'm aware (though I'm not an expert). It is certainly used for one of the many air traffic control units you can encounter at larger airports (e.g "Contact departure on 123.45").
My understanding is that the word 'take-off' over the radio is (or at least should be) treated like a loaded gun, you only say it when you mean it. Departure is used in place of take-off where appropriate (e.g. "Speedbird 101, holding short of runway 13, ready for departure.")
In my experience around towered airports, I can't say I've heard "take-off" used in any radio comms I've had. In the example you've given, "departure" would be used instead of take-off as you've said. Towers are encouraged to use other terms[0], like the following:
"N1234 cleared onto the active runway" which means you're free to proceed with your take-off roll.
When you leave the airspace(at least at a class D airport), the controller will contact you with "N1234 frequency change approved", which means you either contact the next frequency planned in flight(such as flight following, or no frequency if you're just flying around in class E).
