Can varnish affect the performance of the air gap in an SMPS transformer?
Rest assured you may safely assume that the magnetic permeability of varnish is close enough to that of air or vacuum (\$\mu_r \approx 1\$), and yes, the gap size will typically dominate many of the characteristics.

See for example this page, especially the non magnetic materials at the end of the table. Unless your varnish is loaded with metal or ferrite powder you should be fine.