You will need to be present with your luggage at the RAC counter to check in for your flight and check your luggage through to your home airport. Apparently, as long as everybody in your room has the same last name, only one person needs to go with the luggage.
From what I understand, Luggage Assistance makes hourly runs (not as personalized or instant as Bell Services). The adult going to check in should be ready to leave the room before the CM arrives. By the way, tipping is appropriate on the way home - both to the Luggage Assistance CM because they handled your luggage, and to the RAC CM because, well, they're airport employees - the equivalent of SkyCaps - not Disney CMs. In fact, a good way to describe Resort Airline Check-in is it's curbside check-in with the curb thirty miles - instead of thirty feet - from the terminal.
If you don't want the hassle of waiting for a CM to come get your luggage, you can go to the Luggage Assistance counter and borrow a cart, bring it to your room, and bring your own luggage to the RAC counter. You MAY have to leave a credit card deposit for the cart.
You can leave any intended carry-on luggage with Luggage Assistance safely (really - they don't have the time or the privacy to go through personal bags, nor does anyone care to risk their job/reputation/etc) and they'll give you a claim check so you can pick it up when you get back to the resort.
Your Magical Express pickup time will be about 2 PM, give or take fifteen minutes. You will need to be waiting at the stop fifteen minutes before the assigned time, with your entire party and all your carry-on luggage - so if you're not AT the resort, allow at LEAST an hour to get back, pick up your carry-ons, make a last trip to the restroom, and be waiting for the bus. Your assigned time is when it LEAVES your resort, not when it arrives - and the driver won't (can't) wait, and if you miss the bus, Disney won't be responsible for getting you to the airport on time for your flight. There may or may not be another bus along in a half hour; if there is, it may not have room for you.
You only need to physically check out of the hotel if you (a) didn't leave a credit/debit card number to cover expenses and (b) have, well, incurred expenses; or if you left a cash deposit and are due a refund. You don't HAVE to leave any deposit at all, you just won't be able to charge purchases to your room.