Yes,
serving members of the Bundeswehr were allowed to wear decorations issued to them during the Nazi period (including the Iron Cross and Wound Badges, etc.) so long as the decoration did not bear any symbols of National Socialist origin (swastika). The matter was regulated by German law passed in 1957.

The last Wehrmacht member to leave active duty in the Bundeswehr retired in 1984.

See:
www.documentarchiv.de/brd/1986/titel-orden-ehrenzeichen_ges.html

de.wikipedia.org/wiki/Gesetz_%C3%BCber_Titel,_Orden_und_Ehrenzeichen

The Iron Cross as issued under the Nazis did in fact have a swastika on the front, so it remains unclear to me whether any such medals were in fact worn by members of the Bundeswehr.

Iron Crosses issued during the Second World War could be worn by Bundeswehr personnel only if the swastika was first removed from the medal. In some cases the symbol was apparently replaced by a cluster of oak leaves. One account of the funeral of the first postwar German Chancellor, Konrad Adenauer's reports that the pallbearers sported Kinghts Crosses, which is the highest order of Iron Cross. So I would assume that other Bundeswehr soldiers did wear the Iron Cross on their uniforms, though I have no source indicating as much.