It's extremely dependent on all the surrounding factors. For example, my SFO-DCA was recently delayed two hours. It was because they took our frame and used it for something else, and re-assigned a frame which wouldn't be arriving until later. Given that DCA is exclusively a terminal destination for UA, I was comfortable not showing up to SFO until an hour before the delayed departure time.

If a flight posts a delay because its inbound is actually delayed, then it's quite possible ops will pull in another plane if it's felt to be a high priority flight (lots of connections, for example). In aggregate, it's pretty uncommon for a delay to get pulled in, but only because it's also unusual for UA to post a delay at all until they are dead certain they can't get the flight out on time. (Much more common is I'm sitting at home, watching my inbound UX frame stuck somewhere waiting for an SFO arrival slot, and then stuck going to SFO because UA won't commit to posting a delay and yes, swaps could happen.)

That being said, the number of times I've seen a delay get pulled in by 20 minutes to an unreasonable turn time for the arriving aircraft, and the inevitably push back out, is pretty comical.