IDA of a validated numerical model

To my understanding of your question, I feel 'No', if you are talking of scaling the duration of motion (and not intensity). Rather you may identify key ground motion parameters that govern response. This is somewhat judgmental. Scaling should focus on these parameters.
Numerous works of Prof. Nicos Makris and his co-workers who first introduced dimensional analysis to establish remarkable order in in seismic response shall be very enlightening for your problem.

I could not follow the need of using duration scaled motion in experiment. This perhaps complicate the problem unnecessarily. If the experiment is already over, model structure under the scaled excitation may be directly used at this point. For a guideline on scaling for shake table experiment, the following report may be useful:
Hachem, M. M., Mahin, S. A., and Moehle, J. P. (2003). “Performance of circular reinforced concrete bridge columns under bi-directional earthquake loading.” Pacific Earthquake Engineering Research Centre Rep. No. PEER 2003/06., Univ. of California, Berkeley, CA.
By the statement: 'Since, I'm calculating a target response spectrum based on the numerical model, and extracting ground motion based on this target response spectrum (also scaling the ground motions - spectral acc. only), I guess there is no further need for scaling the duration of time history as this acts as a new analysis problem.', I understand that the numerical analysis is no longer intended for validation purpose. In that case, you are right. This is a popular strategy. Yet, scaling ground motion on the basis of spectral acceleration, i.e., multiplying motion by a factor (>1 or <1) is not realistic (refer to Grigoriu, M. (2011). “To scale or not to scale seismic ground-acceleration records.” J. Eng. Mech., 10.1061/(ASCE)EM.1943-7889.0000226, 284–293).