Having done many split stays and/or having to move rooms due to issues (they seem to follow me) I can say the answer is yes for at least own chairs and any other medical stuff. Have stayed at 6 different resorts from where I have moved. Have had my tube feedings even moved for me on a one-on-one level since they are too fragile for Florida september heat.
Have had manual chair moved for me about a dozen times ( along only as back up, being a 24/7powerchair user). Where need be make arrangements the day before like with the feeding bags. Something as basic as the chair, medical equipment etc I would just call bell service when ready for them, wait for them and explain how they can and cant handle the chair (unlike any other seen at wdw so quick heads up does help). Explain bag such and such with the fragile stickers allover it have fragile medical equipment in it and how to handle or not. Tip accordingly and be on my way.
Out of all those times only had one incident last year moving from okw to bw. Eventhough the number of luggage and chair were properly documented, the chair didnt show up. Took some hunting down, apparently snafu at okw where it was left behind. Bw staff went iut and picked it up. Upon delivery found the arm rest broken. Mentioned it, manager bell services got called to the room, noticed the damage, took pics, gave me contact info (late at night by that time) of departement that deals with damages and was promptly contacted the next day.
I opted not to have the part sent to the US given the gouvernment shutdowns in sept last year effected customs backlogs and it mught well taking longer than my 3.5 week stay left. Got a quote from my dealer for the cost of a new armrest and statement it couldnt be fixed, which I emailed to the rep assigned to me. Got the green light right away in writing to buy a new on and getting ir reimbursed incl shipping if I wanted it at wdw instead of back home. Actual last part took some time with rep ill and some other issues resulting in her not able to come over during my stay and take care of the financial then and there. Three days after arriving home it was taken care of though.
Damages can happen, its humans and things can happen. I know from first hand they tend to be extra carefull of aids and medical stuff but risk is never zero. At the same time, find it positive to see a total lack of dicussion or fingerpointing (like airlines do) and a quick visual check from the manager and her picks being enough to trigger a "whatever the costs, we broke it, well pay, just sent me a quote/bill" within the first day.
