Can't say for sure, but probably is, since several of his family members practiced "medicine" in the area. He had a daughter and one or two sons who were "doctors" From what I can figure out, these were not medical doctors like today's, but were more the homeopathic (ecltic) type.
I came across a formula that Dr. David Bates did develop:
Scientific America – page 169 – 16 Mar 1889 issue
"Liniment - David Bates, Bonham, Texas. This liniment is made of linseed oil, turpentine, sulpheric (sulfuric) acid, oil of wintergreen, tincture of button snake root, and other ingredients, to form an antiseptic compound for the treatment of all kinds of wounds, lame joints, etc., and is also designed to act as an insecticide."
Don't know if this is the same thing you are inquiring about.
Bates has been an interesting line to explore. Hoping I can find the burial place.
You can contact me at firstname.lastname@example.org
if you have any other questions.