Does electric current prevent corrosion or oxidation?
Current thru a metal has no effect on corrosion.  However, corrosion is a electro-chemical process, so current into or out of a conductor does effect its chemical activity over surface the current flows into or out of.

This is exactly the effect galvanizing exploits to reduce corrosion of ferrous metals.  The zinc coating does directly protect the metal underneath.

However, the special properties of galvanizing kick in when there is a hole in the zinc protective layer.  Now you have zinc and iron exposed to the same electrolyte.  A current will flow due to this battery.  The direction of the current is such to reduce corrosion of the iron, while instead corroding the zinc.

In some cases, like off shore oil platforms for example, it is cheaper and more effective to put zinc anodes in various places than to coat the steel with zinc.  One advantage is that the zinc electrodes can be periodically replaced as they get corroded away.  In fact they are often referred to as sacrificial anodes.  Divers going down and replacing the zinc blocks is part of routine maintenance.