We use ALMA and JVLA observations of the galaxy cluster Cl J1449+0856 at z=1.99 , in order to study how dust-obscured star-formation , ISM content and AGN activity are linked to environment and galaxy interactions during the crucial phase of high-z cluster assembly . We present detections of multiple transitions of ^ { 12 } CO , as well as dust continuum emission detections from 11 galaxies in the core of Cl J1449+0856 . We measure the gas excitation properties , star-formation rates , gas consumption timescales and gas-to-stellar mass ratios for the galaxies . We find evidence for a large fraction of galaxies with highly-excited molecular gas , contributing > 50 % to the total SFR in the cluster core . We compare these results with expectations for field galaxies , and conclude that environmental influences have strongly enhanced the fraction of excited galaxies in this cluster . We find a dearth of molecular gas in the galaxies ’ gas reservoirs , implying a high star-formation efficiency ( SFE ) in the cluster core , and find short gas depletion timescales \tau < 0.1-0.4 Gyrs for all galaxies . Interestingly , we do not see evidence for increased specific star-formation rates ( sSFRs ) in the cluster galaxies , despite their high SFEs and gas excitations . We find evidence for a large number of mergers in the cluster core , contributing a large fraction of the core ’ s total star-formation compared with expectations in the field . We conclude that the environmental impact on the galaxy excitations is linked to the high rate of galaxy mergers , interactions and active galactic nuclei in the cluster core .