No.
Gouache
gouache. Gouache has more body and dries more slowly than watercolor paint. It is a good medium for creating bright colors and meticulous details and is often used for design and fine artwork.
gouache
Gouache
oil paint on canvas or gouache on handmade paper
Sometimes oil paint sometimes gouache.
Gouache
Gouache
Gouache (from the Italian guazzo, "water paint, splash") or bodycolor (the term preferred by art historians) is a type of paint consisting of pigment suspended in water. Gouache differs from watercolor in that the particles are larger, the ratio of pigment to water is much higher, and an additional, inert, white pigment such as chalk is also present. This makes gouache heavier and more opaque, with greater reflective qualities.
According to Wikipedia, the word "gouache" is defined as a form of colored paint which contains a special binding agent which enables it to be used in opaque painting forms.
You certainly can. It absorbs very evenly into the wood. However, you will have to seal it, as the gouache could reactive or fade. I would suggest a spray clear coat.