We study a mesoscopic ring with an inline quantum dot threaded by an Aharonov-Bohm flux. Zero-point fluctuations of the electromagnetic environment capacitively coupled to the ring, with ωs spectral density, can suppress tunneling through the dot, resulting in a quantum phase transition from an unpolarized to a polarized phase. We show that robust signatures of such a transition can be found in the response of the persistent current in the ring to the external flux as well as to the bias between the dot and the arm. Particular attention is paid to the experimentally relevant cases of Ohmic (s=1) and sub-Ohmic (s=1/2) noise.