If there is a dead zone, then there can in-fact be a phase error. I would think of it more as a phase noise term, rather than an error, since the VCO will be moving around slightly due to random noise. If you can stand slightly higher clock spurs, you can apply a bias so that the phase detector stays out of the dead zone when locked.
This assumes you have at least a type 2 control loop (where there is an integrating element somewhere). If there is not integrator, then you can have a quite large phase error, depending on your open loop DC gain.