Short answer, yes. However, it is important to note that the WSO is not a pilot. The WSO is trained to operate the weapons systems, not fly the aircraft, but does have basic flight controls including throttle, stick, rudder pedals, compass, HSI, etc. He does not have good forward visibility and would likely have to be talked in on final approach by the tower, as his view is obstructed by the pilot's seat.
Although the F-15E was developed from the D-model used for pilot training, the airframe was significantly redesigned for it's new purpose, and the back seat of an E-model bears only a passing resemblance to the back seat of a D-model. The WSO has a very specific and complex set of tasks which does not include flying the airplane, and his controls are designed around that purpose. He has more screens than the pilot to look at, and two side-stick controllers (not part of the flight control system) that are used for controlling / selecting / guiding / programming / etc. a large variety of weapons. He also has primary control over the FLIR and laser pods used for target designation and tracking.
On a final note, it is not uncommon (although less common in these days of sequestration) for non-aircrew personnel to be given 'incentive rides' in the back seat of aircraft like the F-15D/E or F-16D, and during these rides control of the aircraft is invariably passed to the passenger. I was privileged enough during my Air Force career to get a ride in the back seat of an F-15E (tail number 88-1671 at Seymour Johnson AFB, NC) and can say from personal experience that it is possible to fly an F-15E from the back seat. It was the most exhilarating 5 minutes of my life. Fortunately for both of us, the pilot didn't experience any problems during the flight...