The standard merger-driven galaxy evolutionary scenario predicts a phase of deeply “buried” supermassive black hole growth coexisting with a starburst before feedback phenomena deplete the cold molecular gas reservoir of the galaxy and an optically luminous quasar (QSO) is revealed. We present measurements of the cold gas reservoir of a small sample of obscured and highly obscured QSOs at z>1, including well studied objects such as XID2028 and GMASS953 for which the gas mass has been derived through CO SLED modelling. We compare the molecular gas conditions of our targets with those of other systems at z > 1, considering normal and SMGs, unobscured and obscured QSOs from the literature. From the comparison with literature data, we found that, on average, obscured QSOs are associated with high SFE and low gas fraction with respect to normal star forming galaxies and SMGs. We found comparable gas fractions associated with mildly and highly obscured active galaxies. Moreover, the SFE of CT and obscured systems are similar to those of unobscured quasars. These results could be in tension with the galaxy evolution scenario or, alternatively, might suggest that feedback effects are critical from the early phases of galaxy evolution.