The timescale for the DC-8 was entirely too late for the C-135 contract. A better question would have been whether Lockheed, might have been a viable commercial competitor for Boeing if the tanker/transport contract had been split between the two companies?
Oops, I had forgotten about Lockheed, what got me posting the question was this wiki article (I know I know but it is sometimes useful).
Douglas was lukewarm about the jet airliner project, but believed that the USAF tanker contract would go to two companies for two different aircraft (as several USAF transport contracts in the past had done). In May 1954, the USAF circulated its requirement for 800 jet tankers to Boeing, Douglas, Convair, Fairchild, Lockheed, and Martin. Boeing was already just two months away from having a prototype in the air. Before the year was out, the Air Force had ordered the first of an eventual 808 Boeing KC-135 tankers. Even leaving aside Boeing's ability to supply a jet tanker promptly, the flying-boom air-to-air refueling system — as first fitted to the KC-97 — was also a Boeing product: developing the KC-135 had been a very safe bet.
Just four months after issuing the tanker requirement, the USAF ordered 29 KC-135s from Boeing. Donald Douglas was shocked by the rapidity of the decision which, he said, had been made before the competing companies had had time to complete their bids, and protested to Washington, but without success. The U.S. Air Force would buy more than 800 strategic tankers over the next ten years, and every one of them from Boeing. In financial terms, the Boeing 707 would have an armchair ride, while Douglas would be short of cash from that time on.