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.
Bridget Riley uses acrylics and oil paints, gouache and screenprint.
The ideal surface for gouache is cold-press illustration board. It is stiff and unyielding, as opposed to stretched canvas,* and has a perfect tooth. *You don't want the paint to crack and flake off when dried.
Gouache
Gouache
oil paint on canvas or gouache on handmade paper
I use semi-gloss latex.
Gouache
Gouache can be used on canvas or paper, although I would say most artists use it on paper. Gouache and watercolors and acrylics are very similar; the primary difference between gouache and watercolors are that gouache paints are opaque and most watercolors are tansparent / translucent. This is not entirely accurate, however, because highly-diluted gouache paints are translucent as well.
Use a good quality primer that is intended for all paints or for oil based paints. You might want to use a tintable primer (Killz for example), and have it tinted to approximate your final paint color. That gives much better chances of painting in one coat.
Marc Chagall used many materials. He used oil pastels, paints, matte, Bristol board, chargoal, pencils, colouring pencils and many other art equipment.
There is no such thing as gasoline paint.
No, concrete paint will eventually chip and peel away from the wood and eventually rot. Concrete paint does not have the same bonding and protection agents as multi-purpose paints. My advice, go to a home improvement store and buy multi-purpose primer and the shade of multi-purpose paint you want. Just be sure it says "for wood".