Could OST be used to allow multiple companies to share one helpdesk ?
Yes. But if you want custom logos and looks for each company then you would need to do some coding.
Is there any way for a client to be 'pre configured' on OST and allocated to a specific company ?
This would be an involved mod of the OST source. There is a mod in the mod forums that does something similar (sets up authentication for users) that you could use as a base.
Also any way to allow 'staff' members to only see tickets allocated to their specific company ?
This might work:
Assign staff to groups.
Configure which groups can access which departments.
Assign tickets to departments.
Staff would still be able to see un-assigned tickets, but there is a mod in the mod forums for auto-assigning tickets that you could implement that should handle this.