If yes, is there an online source to see the results?
Something like Canonicals usability tests webpage would be nice.
No, there are no usability tests performed by the LibreOffice project / TDF.
It is very hard to not create a biased test anyway - whatever is your desired result, you just design your tasks that way/pick the testing audience accordingly. Especially with a software that is used for so various different task, that differ so much in complexity, and where users’s demography and background is so different, it is nearly impossible to design a useful/fair test that stands critic questions regarding the methodology.
So bottom line: We have an ux-team that does its bests with the currently limited capabilities there are regarding changing/adapting the UI. (currently LO’s UI-layer is not very flexible, but as touch-control interfaces will have to bee added, this layer very likely be revamped as well, making it easier to make larger changes).