Yup...many will but the multi day parkhoppers to use the MM perk and/or get in on what would be a blackout days then upgrade to an AP as soon as practical to take advantage of the AP discounts inside the park which can be substantial on a muti day trip.
Just needs to be upgraded before the end of you last day of eligible use on the multi day ticket to get value towards the AP.
If you are looking to stay on site, you need to call and book the AP rate over the phone if you do not yet have your AP. You do not need to have the AP in hand to book that rate, only present it before checkout day. If you are booking a room and ticket package online you are looking at rack rates, not the possible available AP rates.
If you are indeed stayin on site you get EE every day and if there are no blackouts on the AP you wanna buy during your trip, then there is no advantage to buy tickets then upgrade. Just go right for the AP.