Aims. We present a multi-wavelength study of the molecular gas properties of a sample of local Seyfert 2 galaxies to assess if, and to what extent, the presence of an active galactic nucleus (AGN) can affect the Interstellar Medium (ISM) properties in a sample of 33 local Seyfert 2 galaxies. Methods. We compare the molecular gas content (M H 2 ), derived from new and archival low-J CO line measurements of a sample of AGN and a control sample of star-forming galaxies (SFGs). Both the AGN and the control sample are characterised in terms of host-galaxy properties (e.g., stellar and dust masses, M and M dust , respectively; and star formation rate, SFR). We also investigate the effect of AGN activity onto the emission of polycyclic aromatic hydrocarbon (PAH) molecules in the mid-infrared (MIR), a waveband where the dust-reprocessed emission from the obscured AGN contributes the most.Results. The AGN hosted in less massive galaxies (i.e., M < 10 10.5 M ; M dust < 10 7.5 M ) show larger molecular gas content with respect to SFGs matched in stellar and dust mass. When comparing their depletion time (t dep ∝ M H 2 /S FR), AGN show t dep ∼ 0.3−1.0 Gyr, similar to those observed in the control sample of SFGs. Seyfert 2 galaxies show fainter PAH luminosity at increasingly larger dominance of the nuclear activity in the MIR. Conclusions. We find no clear evidence for a systematic reduction of the molecular gas reservoir at galactic scale in Seyfert galaxies with respect to SFGs. This is in agreement with recent studies showing that molecular gas content only is reduced in regions of subkpc size, where the emission from the accreting supermassive black hole dominates. Nonetheless, we show that the impact of AGN activity on the ISM is clearly visible as suppression of the PAH luminosity.