In theory, the agent will tell you that it will 3-day and some would say a week to have the miles redeposited. In practice, they could put you on hold and they could call MP to have an immediate redeposit. If it is pure UA metal, most of the time it will auto redeposit by the time they finish typing the cancellation.

Best practice is to have your next itineray handy and ask the same agent to cancel and book your next itineray for you. That would force some lazy agent to make the miles are redeposited and then use them to book the new flight for you using those redeposited miles.