Probably not. The long tail provides the balance.
This is how birds and kangaroos work, the body is more or less horizontal, with the pelvic girdle at the center of balance. There are several species of lizards where I live, and when they are REALLY in a hurry, they always run on their hind legs, with a long tail held straight behind providing the balance.
The front legs are held close to the body where they won't get in the way. The head and jaws are very big and heavy on reptiles, and way at the front, and must be counterbalanced.
Primates have lost their tails by adopting a vertical posture and a complex spine, hip and balance arrangement which is quite unique in the animal kingdom.