Does accurate translation estimation using a camera matrix mean the orientation estimation will also be accurate? Pose Estimation of single camera and planar pattern:

If I have an appropriate camera matrix with intrinsic parameters that allows me to calculate translation of the camera relative to a chessboard, for example, and it does so very accurately, does that mean my rotation calculations will also be accurate? 

This may also be considered in the context of the camera calibration documentation for opencv.

References to your answers would also be appreciated.

EDIT:
thanks to @tbirdal for the links
"Pose and position" is an incorrect phrase. Pose is a combination of position and orientation.
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.