Oh, heck yeah. That's where all my driftwood came from because I'm, well, cheap. I can't afford $20-100 for a piece of wood I can find on the shores of the lake! Some people even take deadwood out from the woods and strip off the bark.
Here's the thing: look for hardwoods only. No pine, spruce, tamarack, or woods that are "sappy". Then when you get it home, clean it well to get the obvious stuff off, then you'll need to soak it for a good long while to get it to sink again and get rid of some of the tannins that will leach into the water and turn it brownish. Then follow with pouring boiling water over it to kill any nasties.
If you don't want to wait weeks, pick out a nice piece or six, then just clean it off and pour the boiling water over it. You can force it to stay underwater by attaching it to a piece of flat slate, or putting big rocks on it until it does become waterlogged.
By the way, love your avatar!