Doubt what you like, but I "rescued" old MS Office documents for my grandfather with that. Also this is a common fear when leaving MS Office, so you can bet they work on that. I never had someone complain over OO-compatibitlity until now, so there is that.
When LibreOffice appeared on the stage, that was actually my first test back then: opening an existing ODT document I had written. It was already displayed incorrectly at the time.