If you were flying non stop out of OGG on an AA flight to LAX, SFO or HNL you would be able to check in, either at airport or on line, with AA. Since you are flying on HA from OGG to HNL then connecting on AA to SFO, at OGG you will have to check in with HA. HA should give you boarding passes for your AA flight.
With all of that said, other than my most recent trip to Maui (2008) I could never check in on line with either carrier. I always had to "go to the HA counter". Once in HNL, you will not have to go thru security again. Maybe AG inspection if walking from interisland to main terminal. Not a hassle at all because most take shuttle. I have never seen more than 10 people in line at AG inspection between terminals.
Speaking of AG inspections, once you arrive at OGG hit the AG inspection station prior to checking in. All of your luggage has to be inspected before checking bags.