I actually had a similar delay out of LAX a few weeks ago. Arrived about 30 minutes before the original departure time (2 hour delay) and had no issues with checking luggage, or it arriving with me. I agree with Bartendress that if the notification changes the departure time, it changes the check-in requirements.

As a side note, though, someone did tell me that just because they notify of a delay, they can still take off on time with an equipment change, so you run a risk if you still don't show up at the original time. Seems kind of stupid to me to tell me you are delaying my flight, but then expect me to sit there waiting any way.