When a response spectrum load case is subjected to a DIRECT ANLYSIS, does the software apply the reduction in stiffness like 0.8EA and 0.8*Tau*EI as is required for a DIRECT ANALYSIS ?

Yes the software does apply the 0.8 reduction factor to the area ( A ) and Moment of Inertia ( Ix, Iy and Iz ) but it cannot account for Tau as for that the software needs to know the nature of the axial force which is not possible for a response spectrum analysis because the forces are devoid of any signs. Moreover it would not make sense to apply the Tau-b anyway because the member forces in the various members from a response spectrum analysis are not forces that occur at the same time instant.

It may be worth noting here that one cannot satisfy ALL the requirements of a Direct analysis for a response spectrum load case. The reasons are explained in detail in the following wiki article   

http://communities.bentley.com/products/structural/structural_analysis___design/w/structural_analysis_and_design__wiki/21018.response-spectrum-loading-in-direct-analysis