The official Star Alliance guide only states the following:
Star Alliance Gold
Priority Reservation Waitlist
Priority Airport Standby
Priority Check-In
Additional Baggage Allowance
Priority Baggage Handling
Star Alliance Gold Departure Lounge Access
Priority Boarding
Star Alliance Silver
Priority Reservation Waitlist
Priority Airport Standby
As you can see Business Check-in is not a *S benefit, however some FFPs grant their respective own *S members this benefit. (such as LH FTL being able to checkin at the Business counters)