As a general rule, email doesn't make any guarantees about delivery times since a server could be congested or temporarily unavailable. But our server will process a message and send back a reply as soon as it receives a message. (In fact, our send-to-omnifocus autoresponder never even records a copy of the message, it just processes it in memory and immediately starts sending the reply. Of course, if the place we're trying to send the message back to isn't accepting email there could still be a delay before it's delivered, and during that delay the message would be temporarily stored on our server's disk.)
I did notice that some messages were being delayed by our spam greylisting service (in cases where people hadn't sent any other email to omnigroup.com recently)—for a minimum of 5 minutes, but sometimes as long as an hour or more (depending on how often the sending email server retries failed delivery attempts). I've turned off the greylisting service for the send-to-omnifocus autoresponder now, so that delay should no longer happen.