It's usually pretty quick ... unless something doesn't work out as intended in their computer system. It's not like the cs person with whom you speak mails it from their desk.
I've had a shipping label somehow become lost & wayward. The cs person with whom I was dealing was a bit embarrassed and annoyed ... when I called back he learned I hadn't received the label ... because the computer indicated the request for the slip had been accepted and processed and he had expected it had gone out and already been received by me.
I think they have the ability to email a label, as well, although I prefer to wait for the physical label, myself.
Sub Club #9; .40 S&W Club #1953; S&W Club #3913
Retired LE - firearms instructor/armorer