The answer is yes. The pre-authorized or “Draft Checks” are legal under the Uniform Commercial Code.

Uniform Commercial Code

Title 1: 
Section 1-201 (39) Signed includes any symbol executed or adopted by a party with present intention to authenticate a writing…

Title 3 – Commercial Paper: 
Section 3-401 (1) Any writing to be a negotiable instrument within this title must (a) be signed by the maker or drawer; …

Section 3-401 (2) A signature is made by the use of any name, including any trade or assumed name, upon an instrument, or by word or mark used in lieu of a written signature.

Section 3-403 (1) A signature may be made by an authorized agent or other representative… No particular form of appointment is necessary to establish such authority…