Ok, it seems like it *mostly* works, but I found an interesting bug right away.
The server could not return content for one particular message (nothing unusual about it, very short, plain text, no attachments). My app's workaround code kicked in when this happened, and it all worked out in the end, but it made me wonder if there are any more surprises.
I'm going to contact MS support about it and give it a bit more time before changing the app's preset for Hotmail.
Still great news though.