Does a good staff Officer, make a good Company Commander? How important is this to consider when pairing Company level Command teams?

To be a good well rounded leader one must understand the staff and what goes into supporting the command and the mission. These things are learned being a staff officer/NCO.

Leadership is a whole different ball of wax. A good staff officer /NCO may not make a good leader as leadership traits are much different than staff traits. I will say good leaders usually make good staff officers /NCOs due to the amount of decisions needing to be made, many times without hesitation.

No. Not at all. I have seen staff officers that were great at staff and completely sucked at being part of a command team.
But officers need that staff time to help develop them. In my branch I can tell which CPTs were company XOs and those that were not. The biggest tell is their approach to maintenance.
The biggest fail point I see is the failure to understand as a Commander you are part of a two man team. I have seen great staff NCOs fail at this too in the 1SG seat. You have to be a solid unit when facing the formation and when facing the higher command. When on staff, sure you have a shop, but it is usually just you facing the old man when things go sideways. Some folks can't let that go and it ruins the team

It depends on a lot of things because not all staff officers are good commanders.