Can My Users Sync their Teams Statuses to the Phone System Statuses? 

This is on our roadmap, however, it is not currently possible to do so natively in teams. 

Managing Statuses in Teams

While the ability to do this natively in Teams is on our roadmap, users still can manage their phone system status using the custom statuses feature in 1stream.

This can be done using the 1stream Teams with SSO Application within Teams after adjusting their Microsoft presence.