I think not, but will need to check with examiner friends next week unless someonelse pops on here with the definitive answer
Position fixing on the diversion leg may be by instruments (VOR or NDB) according to JAR but also DME is commonly used and permitted
On your first leg you are meant to be tracking using outside references not radioaids
If your aircraft is equipped with a modest RNAV I advise you to tell the examiner that you will not utilise RNAV unless you are superbly competent with it