Yes that is correct, note that the equation you quote is equivalent to;
v_p = 1/(n*sqrt(e_0*m_0))
v_p = c/n
Phase velocity however is normally written as
v_g = w/k
Where w stands for the angular frequency (omega) and k is the wave-vector (or wave-number in 1D).
Phase velocity is just the velocity of the individual wave components (the velocity of the nodes, crests etc), not to be confused with group velocity which is the speed of the collective wave (or wave-packet).
Claude.