You should definitely paint the foam in an earth colored latex first. The exact color should be about what the earth really looks like in the geographic area you're modeling. For example, in my area of Alabama, the pink color of the foam is a pretty close match to red clay soil. Other areas can range from a slate gray to a deep brown. It will actually look more natural not have ground cover on every square inch since nature always has some bald spots.
Water and white glue will work fine with sawdust but make sure the sawdust is completely dry first. Use the usual mix of about 30% white glue and 70% water with about an ounce of alcohol to break the surface tension of the water. Now, this is the most important. Add three or four drops of bleach for every pint of glue mix. Sawdust contains all kinds of microorganisms that will thrive on water and glue, along with the humidity that's naturally present. The bleach will kill these and prevent you having a horrible stench from all your nice looking ground cover about six months after you lay it down.
Spray the ground cover very lightly with water, just enough t get the very top a little wet. Too much water will make the ground cover run and turn it into a goopy mess. I used to use a medicine dropper to apply the glue/water mix. As long as the mix immediately disappears into the ground cover when your are applying each drop, you've gt it wetted just right. If it sits on top of the sawdust, it need to be wetted just a bit more.
When I first started in model railroading in the mid-60's, colored sawdust was a common ground cover. It doesn't have the irregular look of ground foam and tends to look more like a lawn than natural ground cover. You can correct this by using a small amount of ground foam when the sawdust is completely dry and sprinkling it over the terrain to add some natural variation. Many of the most famous early layouts, including John Allen's, used sawdust for ground cover, and it's still a viable material today if handled right.