If I have two electrodes, one a working, the other a counter electrode
and just make them touch, without the use of an electrolyte or an
ionic conductor, what will happen and why? Will the electrolyte be
needed if reduction/oxidation needs to be done at only one of the
electrodes, without affecting the other?

You need 2 different metals to form a battery because their work
functions are different i.e. there's a potential difference. You
electrically connect them via salt bridge and have two leads having
one cathode and one anode. If you connect the leads together, you
basically short out the positive terminal. Does that answer your
question at all?

Perhaps the working electrode is made of a metal such as zinc and the
counter elctrode is something like copper. I have not previously heard
these terms. When they touch (no ionic conductor) you get a
thermocople, but no current will flow unless there is another junction
at a different temperature in the electrical circuit. If there is an
electrolyte (or some other kind of ionic conductor) the zinc will be
eroded by forming ions, protecting the copper from corrosion, if the
electrodes are touching.
 I don't think either reduction or oxidation will occur unless an
electolyte or other ionic conductor with (or without) the electrodes
touching.
 Hi jaepurvis: An acid or alkali will work as well as a salt bridge.
You don't need to specify positive terminal as it is shorted to the
negative terminal which is the source of electrons. It would be
equally correct to say the negative teminal is shorted.   Neil