First let me say that I haven't actually tried this yet myself nor have I used SuperShuttle but I'm doing research for spending time at Disneyland before my trip too.
From LAX to the port I think it's about 20ish miles. From the port area to DL is about 35 miles (not including any traffic issues).
So I guess what I mean is that it would be somewhat wasted to go from LAX to the port, and then back over to DL and then finally back to the port, a lot of time wasted in traffic. Versus if you were willing to talk with your parents about your idea, they might consider going right from LAX to Disneyland and staying in that area instead. No need to drop off luggage and not dealing with traffic in three seperate instances. Then the next day they could use transportation to get back to the pier.
If they are flying in and won't arrive at LAX until late afternoon Friday and then going to Disneyland before departing on the cruise Saturday, there is just a lot of time that would get wasted. I don't know if they have already booked their flight or not.
So I guess in theory you could pay Super Shuttle to do this but it would be an added expense. In which case it "might" be cheaper to go on Priceline or similar and get them a hotel room close to Disneyland for like $25 or something and have the transportation take them directly from LAX to this Priceline hotel. they wouldn't even have to actually stay there then, just use it as somewhere to store their luggage while they are at Disneyland and then get picked up from that location (there are lots and lots of hotels within walking distance of Disneyland).
If your parents wanted to share a Super Shuttle from LAX to Disneyland, it would probably cost them about $35. Do you know how they intended to get from the airport to their hotel in the first place?
Renting a car would be a cheap option if they were willing to drive because again, they would have somewhere to store their luggage while at Disneyland. It sounds to me like they would get more enjoyment out of this whole process if they were to arrive on Thursday for a Sat departure.
I hope someone else has more info to share!!