Order started when I arrived to pick it up, not when I submitted it online--as far as I could tell. The total time elapsed between ordering and getting my food was almost 45 minutes. The food was great in every respect, but I won't be ordering online again, especially if I'm in a hurry.
I visit this restaurant frequently and they never take this long, and on that day they weren't busy. Conclusion: they either didn't notice the order, or they didn't want to start it before I paid in person.