Muddling if you suspect ASD, I would just start implementing the support strategies you would use if he had a diagnosis. They can't do any harm and believe me, it will really help lower your stress levels and probably his too.
Ds1 is 13 and has AS. We are heavily involved in his organisation and planning, both in terms of bag packing and homework. He has to give me or dh his planner as soon as he walks in the door and we work out what needs doing when together. Then, after his snack and computer time (computer time destresses him after school and a long taxi ride home) he has his tea and we remind him what he needs to do homework-wise and make sure we keep a check on him throughout. After that we pack his bag together. He always answers 'none' when I ask what homework he has been set, but it's very rarely true. He's not being obstructive, his poor executive function means he doesn't find it easy to recall what happened when over a period of time. Invariably it will be that there was no homework set during his last lesson and that's as far back as he's thought.
I find it useful to write a small note on the day his homework is actually due in, as well as the day it's set to remind us both he needs to take it in that day. I still despair sometimes as he'll swear to the teacher he doesn't have it, when we put it in his bag together the night before and checked again in the morning, but they won't go into pupils' bags, so he gets into trouble when he had it all along. It is exhausting.
Checklists don't work for ds1, he needs a checklist to remind him to check his checklist
and according to his old outreach teacher, that's fairly common. Visual prompts, backed up by verbal prompts and reminders do help though. Ds simply doesn't have the executive function necessary to organise himself, so he needs us to help him, if/when he ever reaches the point where he seems to be more capable, we will change the way we support him, but in the meantime he has enough to deal with and we live in hope that the repetition of doing it all with us will eventually help him learn some good organisational habits.
If he's going through assessment, I would also stay in regular contact with his Form Tutor and Senco and if possible his teachers as well, so you can query any homework issues and chase up lost PE kits etc. After two years we're in quite a good rhythm with it now and it is so much less stressful than dealing with constant missed homework, lost equipment etc.
Ds2 on the other hand, is pretty self-sufficient with 99.9% of his homework now and seems so far to be pretty good at planning what needs doing when and getting it all handed in on time. I did it with him for the first few weeks, then it just kind of drifted into him doing more and more himself, until he was doing it all. I do still ask him what he has each day and he's honest. I think he's come to me a couple of times when he's felt overloaded and couldn't see the wood for the trees and we've talked through a plan of action, but that's been rare.
Having said all that, I have, somehow, managed to agree to help him and a friend make a motte and bailey cake for their History project. It's not really a problem, as cake decorating is one of my hobbies, I'm just worried about making sure it's all their work, not mine, because I know I will find it hard to stand back and let them make a mess get on with it. Ds is going to his friends' house tomorrow, to plan it out and come up with what ingredients we need, then ds and I will bake the cakes and his friend can come over and assemble the whole thing with him later that day. I swore I wouldn't do it and I hate having friends over, but somehow he managed to charm me. 