  We report on IRAM-30m/EMIR observations of 38 red Herschel sources in 18
Planck-selected protocluster candidates (PHz). We detect 40 CO lines on a total
of 24 bright Herschel sources in 14 of the 18 PHz fields. The measured average
redshift is <z>=2.25. We measure redshifts for multiple Herschel sources in
eight PHz fields. In half of those fields we detect from two to three objects
at similar redshifts, supporting the idea that they contain high-z
protoclusters. The detection of sources at different redshifts demonstrates
that foreground and background sources also contribute to the total sub-mm
emission. We compare the properties of the molecular gas, and of the star
formation activity of our sources with samples of normal star-forming galaxies
(SFGs), sub-mm galaxies, and CO-detected cluster and protocluster galaxies at
similar redshifts. We find that the PHz-IRAM sources are mainly normal SFGs,
with only ~20% undergoing a starburst phase. The PHz-IRAM sources are
characterized by star formation rates and gas masses that are, on average,
eight and five times higher than those typical of normal SFGs at similar
redshifts. Their dust temperatures, and depletion timescales are instead
consistent with those of normal SFGs. The analysis of the CO spectral line
energy distribution, available for ten sources, peaks at Jup=3 in most of the
cases, implying low gas excitation. These properties imply that a significant
fraction of the PHz-IRAM sources contains extended, and cold molecular gas
reservoirs at low excitation, and that their star-formation is driven by
secular processes. Multiplicity and moderate gravitational lensing might also
play a role in producing the observed properties. We find that the highest
star-forming protoclusters drawn from the large volume simulations, have
similar SFRs as the PHz protoclusters, but separate out into a larger number of
SFGs. (Abridged)
