You can edit the html code that the editor outputs in SPD's code view but so far not the underlying master page, page layouts or gadgets.
"Not supported in 365" has come to mean MSFT won't be held liable for anything you break, but I've never known them to refuse support no matter what the problem. Understandably they don't want to address custom code issues or things that aren't part of the standard tools.
You can upload web pages but to work with the public site they have to have been created in a 365 editor or the controls used have to match up perfectly with a standard page - and they have to be uploaded to the Pages library.
You may also be interested in this - look under "All Posts" for the article :
Add 3rd party designed pages to your 365 public site