No. If you select the inner table, you effectively select all its contents, and when you paste that into a table cell, the contents of those cells are - as far as possible - distributed between existing cells of that table. This is not what you want, of course.
Instead, you need to select not the inner table but the cell of the outer table containing it. I think that in order to do this you need to have something - even just an empty paragraph - outside the inner table and before it. Then you can select the cell of the outer table either by dragging the cursor, or using Edit | Select All (or Ctrl+A), or using Table | Select > | Cells. Once you have this selection, you can copy it and paste it with the effect you desire.
If you have nothing before the inner table, you can add something in order to effect the copy and remove it afterwards, of course. You cannot add an empty paragraph simply by pressing Enter, as you cannot position the cursor where it would need to be to achieve this. Instead, put the cursor at the very beginning of the first cell of the inner table and press Alt+Enter.
I trust this helps.
Brian Barker