I would concur but bake the transformer in an oven first to drive out moisture, and heat the whole thing - soak at ~200 F for a few hours. Then dip the hot transformer in varnish and suspend it for a minute or two in the pail. Let cool in a warm dry place. The transformer retains enough residual heat to have the varnish set quickly.
The heat thins the varnish and as the laminations and coils cool, the air contained in the interstitial spaces contracts and sucks in varnish.
If one is really going to get into the business of winding 60 hertz/audio transformers, a flea market quality pressure cooker or canner can become a vacuum oven/impregnator.
I wound a large induction coil and used a pressure cooker to vacuum impregnate it with hot paraffin wax - worked like a champ.
Right now I'm building some coils on a winder with a chilled epoxy coating - the mandrel is non-stick polyethylene with a light oil coating and the finished coils look superb.