I don't think there would be any trouble. A bit of a pain, but nothing more than that. If it means adding Disney days, I'd definitely do it.
If you're doing it at the beginning of your trip, some tips I have that might reduce the chaos/stress....
Have your Day1-3 stuff together either in a separate suitcase/bag so you don't even need to take the Day 3-8 days' stuff into the hotel with you. Or if you do take it in for safety reasons, you don't have to unpack it.
I'd try to wait to get any souvies until you are at your BW, so you don't have to transport it.
Talk it up that after xx day "we're going to somewhere new". Be very positive (even if you're stressed by the possibility) and prepare them for the change, and that it doesn't mean you're leaving Disney.
If you're needing crib, try bringing your own portable to provide continuity. I also always brought my own sheets/blankets even when I used hotel cribs because it was familiar to them. I actually did the blanket thing even into toddlerhood for them whenever I could.
Something my DH and I have always done is the AM we're checking out, I get up and do all the organizing, getting everything packed up and ready to go while DH takes the kids somewhere, when they were younger it was breakfast or a walk in the double stroller, since they've gotten a bit older, it's the pool. When he gets back, everything is all ready to go, except perhaps tossing clothes on the kids post-pool, and we load up the vehicle and head out. To the kids it's all seamless, and either (a) I don't get stressed because they're not there getting into everything or (b) if I do get stressed they don't see it or (c) both of the above!
