The only restriction I could see is if your stroller did not fit within the wheelchair spots. Pretty much all strollers will, unless you have a huge double/triple stroller or something like that. You should not have a problem.
Some people find that strollers sit too low for the child to see well from the wheelchair spots (strollers are sometimes much shorter than the theatre seats), so if you end up wanting to transfer, you can do that too.
I am not sure about Nemo but depending on the show, sometimes you have to get there very early to get a wheelchair spot, as opposed to a regular seat. Someone here should be able to tell you how early to get there if he cannot transfer.
Also something to know is that sometimes the number of people who can sit with him will be restricted, usually to 3 or 4 members of the party. The rest of the group will generally sit in the row in front of the wheelchair spots. In American Adventure, it is 1 person. Everyone else in the group must sit elsewhere. I mention this because sometimes autistic children become anxious if the family splits up, and he may do better if he is prepared for it.
Some shows (actually most I can think of) have two wheelchair spots next to each other, with family on either side. This means that there could be a stranger in a wheelchair or
scooter sitting to the far side of your child. At least one person will always be allowed to sit next to your child, but your family will not be able to surround him - there may be a stranger sitting next to him. Also something some children do better to know about ahead of time.
Hope this helps. The only venue I have ever seen CMs really try to get people to transfer if they can is American Adventure and Festival of the Lion King - those two have very few wheelchair spots. You would still be allowed to use the stroller as wheelchair, absolutely, this are just the only two shows I have ever been in where they ask more than once if I can transfer to a regular seat.
In both of those theatres, if you do keep use the wheelchair spots and think your child may need to exit early, tell a CM as soon as you get to the waiting area - it is hard to get out of the AA theatre wheelchair spots unless you are on an end (same as the regular seats - it is a huge theatre) and due to the nature of the Lion King show (theatre in the round-style), there are some spots that you may not be able to leave in the middle of the show.
Sorry my posts tend to be long - I try to answer all the questions I can think of at once. The short answer is that you can use a stroller as a wheelchair anywhere a wheelchair can go, with the exception of transportation (he must get out of the stroller on buses) and I am not sure with the wheelchair vehicles on rides, but I think he needs to transfer for those too.