It may not be quite that simple. Flat maps of spheres always have distortion. (Look up "spherical conformal mapping".) So circles on your map won't be the same as circles on the sphere. In addition, the type of projection used will affect the conversion of your planar coordinates to your spherical coordinates.
I'd suggest you find out what your error tolerances are, the largest distance you're going to be interested in, and what sorts of maps you'll be using.
When your only tool is a hammer, all problems look like your thumb.