Well the G3 is realy a German (H&K) copy of the Spanish CEMTE (not sure of spelling) wich itself is a modernised version to the German WW2 STG-45 wich was experimental at the end of the war. The development was sent to spain before Germany surendered. The CEMTE can fire high pressure loads but the bolt head had to be replaced wich was done when Spain joined Nato.
So that makes the G-3 a Spanish(CEMTE) origonaly, not so much German.

So ,Yes you can fire standard Nato loads in the G-3 But not the Spanish rifle unless modified with a new bolt/breach block.

The reason for Spain to use a low pressure 7.62 was so it was contolable on full auto. The reason why the bigger standard rounds (3006, 7.9X57) were replaced in the fist place.