If one has a pn-junction in a semiconductor light-emitting diode,
where the p-type and n-type materials are connected to electrodes
(conducting material, eg. copper or silver), could the conducting
electrode material on the n-side of the diode also act as the n-type
material itself, since both, the conducting and the n-type material
can transport electrons? In other words, could the n-type material
simply be replaced by a normal metal conductor? If not, why?

I believe you are talking about a "Schottky diode".  Read up on them:
://www.google.com/search?hl=en&q=schottky+contact&btnG=Google+Search

The n-type material cannot be replaced by a metal conductor simply
because it is not a semiconductor. n- and p- type materials are
semiconductors (silicon, germanium, gallium, arsenide) with impurities
(boron, etc) which cause an abundance of either holes or electrons.

This is not a Shottky diode. A Shottky diode is the fast version of a
regular diode, which is not an LED.

In an LED:
1) The longer lead is the positive one.
2) The bitter piece of metal inside the LED is attached to the
positive lead and the tap on top is attached to the smaller metal
piece and the shorter lead.
3) The p- type semiconductor is the base of the LED.
4) There is a small area with n-type semiconductor to which the tap is attached.

Since you have this interest, I suggest you pick up some literature at
your local RadioShack and learn about PNP and NPN transistors.