Q: Is it possible to use the software version of pages with the online version?

I know that google docs has a feature where everyone who has access to a document can edit it simultaneously and everyone can see the edits as they are made. To me, it looks like the iCloud.com pages is the same too. I was wondering if a Microsoft user could go online with his apple id, sign into iCloud.com, open a pages document I shared with him with iCloud pages, and edit simultaneously with me, who has the software version of pages on my mac. I want to be able to see the edits he makes on the pages application. If this is not possible, would I have to go to iCloud.com as well?

Thanks in advance!