Right on! I offer a 4 hour gig extra called “Super Express Pass - MESSAGE ME FIRST”.
Obviously I can’t deliver in 4 hours if I’m sleeping. So I make sure they message me. One guy didn’t message me first (out of 50 or so who have used that option), but I just did it as soon as I woke up, and he didn’t complain.
(I immediately messaged him saying he should have messaged me first, it’s morning in my time zone, and I’m dropping everything to get it back to him ASAP.) Worked great, and he’s ordered from me since that time too.
Anybody can offer something similar, just like @emmaki. In your category it may be less than a day, or a week could be expedited service.
The right thing is to be sure you charge enough for it to make it worth your while.
I don’t see it as a standard option, but certainly something you can add if it works for you.