Does Turbo Tax for business handle Estate Returns for States (specifically Illinois) in addition to the Federal 1041?

Yes, according to the Forms Availability table for TurboTax Business, the software does support both a federal fiduciary/estate Form 1041 and an Illinois Form IL-1041 tax returns.

Yes, TurboTax Business supports Illinois fiduciary (estate/trust) returns.

See https://care-cdn.prodsupportsite.a.intuit.com/forms-availability/turbotaxbusiness_il_windows_fiduciary.html