Are cold flows detectable with metal absorption lines?
[Abridged] Cold gas flowing within the "cosmic web" is believed to be an important source of fuel for star formation at high redshift. However, the presence of such filamentary gas has never been observationally confirmed. In this work, we investigate in detail whether such cold gas is detectable using low-ionisation metal absorption lines, such as CII \lambda1334 as this technique has a proven observational record for detecting gaseous structures. Using a large statistical sample of galaxies from the Mare Nostrum N-body+AMR cosmological simulation, we find that the typical covering fraction of the dense, cold gas in 10^12 Msun haloes at z~2.5 is lower than expected (~5%). In addition, the absorption signal by the interstellar medium of the galaxy itself turns out to be so deep and so broad in velocity space that it completely drowns that of the filamentary gas. A detectable signal might be obtained from a cold filament exactly aligned with the line of sight, but this configuration is so unlikely that it would require surveying an overwhelmingly large number of candidate galaxies to tease it out. Finally, the predicted metallicity of the cold gas in filaments is extremely low (\leq 0.001 Zsun). Should this result persist when higher resolution runs are performed, it would significantly increase the difficulty of detecting filamentary gas inflows using metal lines. However, even if we assume that filaments are enriched to Zsun, the absorption signal that we compute is still weak. We are therefore led to conclude that it is extremely difficult to observationally prove or disprove the presence of cold filaments as the favorite accretion mode of galaxies using low-ionisation metal absorption lines. The Ly-alpha emission route looks more promising but due to the resonant nature of the line, radiative transfer simulations are required to fully characterize the observed signal.