Does the economic calculation problem apply to so-called "market socialism"?
Can prices for factors of production come about? If not, then the problem of economic calculation applies.
Yes, any time a bureaucrat (Or even a monopolist) can bypass even a somewhat freemarket based pricing system then those folks will experience the Calculation Problem as they will not be able to determine the best uses of scarce productive resources.
Please see Rothbards book "Man, Economy and State" chapter 9 section on Calculation Chaos.