  (Abridged) The stellar metallicity, [M/H], may have important implications
for planet formation. In particular, Kama et al. proposed that the deficit of
refractory elements in the surfaces of some Herbig Ae/Be stars (HAeBes) may be
linked to the presence of disk cavities likely caused by Jovian planets that
trap the metal-rich content. This work aims to provide a robust test on the
previous proposal by analyzing the largest sample of HAeBes with homogeneously
derived [M/H] values, stellar, and circumstellar properties. [M/H] values of 67
HAeBes were derived based on observed spectra and Kurucz synthetic models.
Statistical analyses were carried out aiming to test the potential relation
between [M/H] and the group I sources from the spectral energy distribution
(SED) classification by Meeus et al., associated to the presence of cavities
potentially carved by giant planets. Our study robustly confirms that group I
sources tend to have a lower [M/H] than that of group II HAeBes. A similar
analysis involving SED-based transitional disks does not reveal such a
relation, indicating that not all processes capable of creating dust holes have
an effect on the stellar abundances. We also show that the observed [M/H]
differences are not driven by environmental effects. Finally, group I sources
tend to have stronger (sub-) mm continuum emission presumably related to the
presence of giant planets. Indeed, literature results indicate that disk
substructures probably associated to their presence are up to ten times more
frequent in group I HAeBes. We provide indirect evidences suggesting that giant
planets are more frequent around group I/low [M/H] stars than around the rest
of the HAeBes. However, the direct test requires multiple detections of forming
planets in their disks, so far limited to the candidate around the metal
depleted ([M/H] = -0.35 +- 0.25) group I HAeBe star AB Aur.
