yes, Delta will call you and if memory serves me correctly PMUA called me a couple of times as well in similar cases. The new UA won't call and the auto-rebooking feature is known to be terribly broken.
That being said my experiences when calling in such situations has been very good recently (not so much in the beginning) where agents were very willing and able to get me onto flights sa long as there was at least Y1 or F1 available. Don't think UA will do anything is a Y0F0 situation and while I have heard stories that DL is able to do this, I can tell from my experience that it is extremely rare.