My flight departing in 7 hours, and I want to cancel, will they contact me in time?

I have a flight departing in about 7 hours, and I just submitted the refund request form.

For anyone who’s been through this with Emirates, how long did it take for them to contact you? Is there any chance they’ll get back to me before my scheduled departure time, or should I expect it to take longer?

I’d really appreciate hearing about your experience. Thanks!