Primer is mandatory for optimal results.
I frequently paint engravings on wood and acrylic (typically lettering). If I don’t prime it first, results are always suboptimal. For acrylic, the coat of paint will be “thin” wherever there’s a sharp corner, like the edges of the engraving. Surface tension also tends to draw the paint away from the vertical faces below those corners. The underlying acrylic color is visible through the paint in these areas. For wood, there’s a lot of charred material in the engraving that lifts out and mixes with the paint, changing the color.