By “watercolors”, I am assuming that you mean artists paints.
It would be easy to test.
I sometimes tint polyacrylic varnish with water soluble colorants.
Small amounts of water-soluble aniline dye or even the household Rit brand dyes will work.
I would avoid mixing any kind of water-based paints with polyacrylic varnish because of possible chemical problems that might cause the polyacrylic to cloud or even not harden properly.
Artists watercolors generally contain gum arabic or some other form of binder.
Regular water-based latex and acrylic paints contain pigments, opaque additives and hardening agents.
They are designed to hide the original surface.
Again, it would be easy to test.
The main reason I want to tint polyacrylic varnish is to create a transparent toner, not an alternative to an opaque paint. I use tinted finishes to add a hint of transparent color, not to hide the underlying grain and natural wood patterns.
Experiment and see what happens.
It could be neat.
I was a chemist in a former life.
-- Randy (P), rustic wood crafts, Morning View, Kentucky