Yes, I have done it for years successfully to my past Basenjis. I just got a new tri Basenji, Buddy (8 months old) on May 22nd and he lets me brush daily. You have to introduce the brush gradually. I use a cup with water and a soft tooth brush from any stare like Target. I buy 4 packs because he'll chew on them right now and I can toss out after 1 week. I use only water in a plastic cup and dip the brush in the water and let the B lick and chew it a little at first. Gently move the brush around so she can get used to it. Try only this for the first week. Have the her on the couch and sit next to her, on the left if you're right handed and opposite if left handed. Then if the dog seems OK try putting your left hand GENTLY and LIGHTLY over the muzzle and gently lifting the upper lip a little to gently brush the sides of the upper teeth. I only do the upper teeth. If she pulls back don't force it just keep the brush wet because they love to lick anything wet and just let her lick and lightly chew it. Remember don't force it and talk to her telling her what a good dog she is. Try to make it seem desirable to get that wet brush. If she squirms a bit and twists her head just go with the flow and twist with her. Swish the brush in the water to clean it as you go along and keep it wet. Keep it short too. End off on a good note so that it's a good experience.
Note: I never used doggy tooth paste because it upset their tummy and water seemed to work as they like to lick that wet toothbrush.
Remember: Keep it gentle and short and never force it. Always keep that hand that's over the muzzle that lifts the lip light. I did my last 2 Basenjis teeth almost daily all their lives with no problem. My new guy enjoys it and when I swish the brush on the way over to the couch he comes right over to me and I always start with the licking and light chewing.