I think LOC and GS are considered managed modes as per definition because the ILS is selected in the MCDU and FMGC uses it through that. If there was no ILS selected and was flown by tuning the frequency in RAD NAV it will be considered as selected. Also for managed descent lateral managed includes LOC* and LOC along with NAV. That is why appears confusing. Further in airbus there are two functions that help prevent overshoot of localiser i.e.
LOC convergence function: this requires NAV mode and it keeps converging track of 20 degrees from LOC axis.
Enhanced LOC capture: This requires GPS primary it starts the capture using FMS data by turning with 15 degrees convergence before LOC becomes alive.
Obviously with NAV accuracy low these functions will be lost.