  We present a pilot study of the atomic neutral hydrogen gas (HI) content of
ultra-diffuse galaxy (UDG) candidates. In this paper, we use the pre-pilot
Eridanus field data from the Widefield ASKAP L-band Legacy All-sky Blind Survey
(WALLABY) to search for HI in UDG candidates found in the Systematically
Measuring Ultra-diffuse Galaxies survey (SMUDGes). We narrow down to 78 SMUDGes
UDG candidates within the maximum radial extents of the Eridanus subgroups for
this study. Most SMUDGes UDGs candidates in this study have effective radii
smaller than 1.5 kpc and thus fail to meet the defining size threshold. We only
find one HI detection, which we classify as a low-surface-brightness dwarf. Six
putative UDGs are HI-free. We show the overall distribution of SMUDGes UDG
candidates on the size-luminosity relation and compare them with low-mass
dwarfs on the atomic gas fraction versus stellar mass scaling relation. There
is no correlation between gas-richness and colour indicating that colour is not
the sole parameter determining their HI content. The evolutionary paths that
drive galaxy morphological changes and UDG formation channels are likely the
additional factors to affect the HI content of putative UDGs. The actual
numbers of UDGs for the Eridanus and NGC 1332 subgroups are consistent with the
predicted abundance of UDGs and the halo virial mass relation, except for the
NGC 1407 subgroup, which has a smaller number of UDGs than the predicted
number. Different group environments suggest that these putative UDGs are
likely formed via the satellite accretion scenario.
