Brain volume has a good relationship with the overall surface area measured in native space (so, irrespective to any kind of interpolation). We found an R^2 of 0.856, which is higher even than the correlation of brain volume with gray matter volume as measured via VBM-like methods.
However, even if the relationship between these measurements were poor, include brain volume as a covariate hardly hurts the model, unless you have only few degrees of freedom (say, a tiny number of subjects).
Another thing, and perhaps better, is to consider using global surface area instead of brain volume as a covariate for a study of surface area, to remove global and focus only on local effects.