Just to refer to the original question:
is any difference in using Approach Mode or Nav Mode when intercepting and then tracking a VOR radial on an instrument approach
Yes there is a difference. In approach mode it will track the VOR (as accurately as it can), but in NAV mode it will follow a calculated track, based on the known VOR position, using its normal navigational mode, which varies from type to type (and variant) but nowadays is normally heavily GPS biased.
If the approach involves flying directly over the VOR, which is often the case, then it is generally preferable to use NAV mode as it will not then involve negotiating the 'cone of confusion' over the beacon.