First of all my apologies for writing this so late.
My special thanks to John Scranton, who explained things in a nice way. I also thank Doug, Richard, Russell, Skraba and kuppuswamy.
Yes, it is possible to copy a model with its drawing. set parameter in option file: RENAME_DRAWING_WITH_OBJECT=BOTH Now when an assembly or part is copied by 'save as' option, it will create copy of drawing as well with a name same as new part/assembly name. But only concern I found here is that if I copy a part with new name, it will try to copy a drawing file that has name same as partfile name. It did not look for associativity. This may go illogical at times when the part file name and its drawing file name are not same and at the same time there exists a drawing file with name same as part name, then, a wrong file will be copied. So, always have a drawing file name same as part or assembly file name.
What parts to rename can be decided in 'save as' dialogbox. If part drawings are contained with assembly drawing then the new drawing will now point to renamed parts, which is required most of the times.
If part drawings are lying some where else then we have to take another route, which are better suggested by all those who replied. All replies are put here as received.