Can a galaxy redshift survey measure dark energy clustering?

(abridged) A wide-field galaxy redshift survey allows one to probe galaxy clustering at largest spatial scales, which carries an invaluable information on horizon-scale physics complementarily to the cosmic microwave background (CMB). Assuming the planned survey consisting of z~1 and z~3 surveys with areas of 2000 and 300 square degrees, respectively, we study the prospects for probing dark energy clustering from the measured galaxy power spectrum, assuming the dynamical properties of dark energy are specified in terms of the equation of state and the effective sound speed c_e in the context of an adiabatic cold dark matter dominated model. The dark energy clustering adds a power to the galaxy power spectrum amplitude at spatial scales greater than the sound horizon, and the enhancement is sensitive to redshift evolution of the net dark energy density, i.e. the equation of state. We find that the galaxy survey, when combined with Planck, can distinguish dark energy clustering from a smooth dark energy model such as the quintessence model (c_e=1), when c_e<0.04 (0.02) in the case of the constant equation of state w_0=-0.9 (-0.95). An ultimate full-sky survey of z~1 galaxies allows the detection when c_e<0.08 (0.04) for w_0=0.9 (-0.95). We also investigate a degeneracy between the dark energy clustering and the non-relativistic neutrinos implied from the neutrino oscillation experiments, because the two effects both induce a scale-dependent modification in the galaxy power spectrum shape at largest spatial scales accessible from the galaxy survey. It is shown that a wider redshift coverage can efficiently separate the two effects by utilizing the different redshift dependences, where dark energy clustering is apparent only at low redshifts z<1.