Patton probably did read Rommel’s book, put it was on company and battalion level infantry tactics rather than armor tactics & operations. However, it would have given Patton an insight as to how Rommel thought of fighting.
In 1928 Patton did a study of tables of organization and equipment for an infantry rifle company, battalion, brigade and division. His studies resulted in a great reduction in the size of a division with far greater firepower and effectiveness. The end result was the “triangular” division of WW II.
Patton was ahead of his time. And ahead of Rommel.