No, you cannot copy and paste the conditional format.
I usually use this trick.
1. Bring the object include conditional format to the same layout.
2. Bring it to the front ( It should be when you paste its object now, but you'll need this if it's there since before. ).
3. Select muti objects and open conditioanl formatting dialog.
4. It shows you the settings you want to paste. Just select OK.
Thanks for the great tip Shin! It worked like a charm for what I was working on tonight.
I'm still thinking that from an intuituve point of view, Copy/Paste functionality is a little more user friendly and expected since they implemented the copying and pasting of object styles.