It has been used that way, most markedly by AOL back in the early '00s, but is really isn't used that way, at least in the US, or at least in the parts of the US where I have lived.
Some people may understand your meaning, others wouldn't. If you were to ask me to "mail" something to you, I would be confused, and take a few seconds to catch on. But if you said "email", I would immediately know what you mean.
So ultimately, it's a matter of clarity. Use "email". It isn't saving you any time to say "mail" instead, and you probably save time, since you don't need to wait for the other person to catch on.
Both are grammatically correct.
Yes, you can use such words as tomorrow, this evening, later today, next month, five years from now in sentences that refer to future time.
But there is no "future form" in English. The simple present tense form of to leave is leave/leaves (he leaves); the simple past tense form is left (he left); the simple future tense form is ??????. English does not have one.
If there were a future tense form of leave we could just write it, something like leavek (he leavek).
To say will leave is the future (tense) form is to arbitrarily choose one of over a dozen ways to refer to future time as "the future form".
Actually, the modal will expresses current resolve:
I will leave for New York tomorrow
expresses the current resolve of the speaker to leave for New York tomorrow. As such, it is a promise. Even such statements as The sun will rise tomorrow and That kind of thing will never happen here are promises.
Thus
I don't know when he'll (he will) leave tomorrow
expresses the speaker's ignorance of the exact time tomorrow that the person he will fulfill his resolve to leave. He has made his resolve known, but perhaps he has not stated at what time tomorrow he will carry it out.
We use the simple present to talk about future time with the strongest certainty. Things we are absolutely convinced to happen:
The sun rises tomorrow at 0626.
The train arrives tomorrow.
He leaves for New York tomorrow is the way to say with the strongest certainty that in the future time designated 'tomorrow', the person he => /leave/ for New York.
Thus
I don't know when he leaves tomorrow
expresses your ignorance of the exact time that his leaving happens. You know he's leaving tomorrow, just like you know the sun's rising tomorrow, but you don't know when tomorrow or at what time tomorrow.
How else can we refer to future time? Here are some ways:
He's leaving for New York tomorrow.
He's going to leave for New York tomorrow.
He's going to be leaving for New York tomorrow.
He'll be leaving for New York tomorrow.
He is to leave for New York tomorrow.
There are others.
Best Answer
If this is all you say, it might be considered rude. It can sound like you expect or are entitled to leave early. Also, it seems vague. I would recommend that you include the reason that you need to leave, if possible. I understand that the reason might be a private/personal reason, but the person from whom you request permission might require some proof.
You might consider