If memory serves me correctly, the slug is connected to the cathode (negative) side of the LED. (It's positive in the red/amber ones).
Strictly speaking, no, you wouldn't need to isolate them. However, I have no idea if in the long term not doing so would be harmful to the LED - and I'm not in a position to find out. So if I were you, I'd isolate them anyway.
Isolating the slug is pretty simple, just use some form of thermal epoxy which isn't electrically conductive. I believe some people have had success with the use of "Sharpie" markers as an electrically isolating coating as well, without compromising thermal conductivity.
No doubt, others will be able to answer your question a lot more thourghly though!