Hi everyone. I take it back, the "layered navigation" (LN) does work even on imported configurable products. I just couldn't grasp the concept...well the way it works. I'm having the option "FilIterable (with result)" on all 3 attributes. LN checks for each of them (type,color,size) in my case, if they will reduce (narrow) the collection of products when user clicks any value in attribute. I've attached a sample bellow to illustrate the concept. The attribute "Type" has "S" and "R" options, but in LN only "R" is displayed, because if user would select "S", the result would be all 3 products in store and that would not help narrow the selection.
So in my case, all imported configurable products had all "types" all "colors" and all "sizes" at disposal, so that's why the LN didn't show up. If an attribute doesn't help the user to narrow the total selection, that attribute is not show in LN, and if this happens to all attributes, then the entire LN is hidden.
As much as I've tested that's all, and the question could now be marked as solved and should end with the answer from Donnie.