Does accurate translation estimation using a camera matrix mean the orientation estimation will also be accurate?
If you pose estimation algorithm carefully minimizes the reprojection error using the standard non-linear techniques e.g., Levenberg Mardquardt, and your corner detection scheme is sufficiently accurate in the subpixel level, then yes. I would expect the residuals to be very small. Of course take into account the distortion parameters; they have to be calibrated as well. If you are using OpenCv and referring to the standard functions such as findExtrinsicCameraParam, then you are good to go.

The problem is also known as PnP due to the correspondences. Lepetit et. al. review it nicely here.

Also, Grest et.al provide an overview of 3 methods here.