The B-36 Peacemaker had 6 radial engines, driving 6 propellers, AND 4 jet engines in 2 nacelles. The jet engines were used for takeoff and for "dash" over a target. The jets were turned off during cruise because they used considerably more fuel than the piston engines.
As such, they HAVE made propeller/jet hybrid aircraft in the past, though not electric.
To answer your questions:
You probably want to feather the propellers and kill the electric motors. If the props can only drive you to 250 MPH, leaving them windmilling in the slipstream when the jets are running will add drag, which will only serve to hurt your cruise speed and/or increase your fuel consumption.
They only work in conjunction as speed BELOW what your props can drive (eg 250 MPH, in your example). Beyond that, if it's speed you're after, you're better off without the props.
At speeds above what the props can deliver, they're essentially small windmills. And not very efficient ones at that.
Now, what WOULD be helpful as a "hybrid" aircraft would be a gasoline engine, turning a prop, with an electric motor added between the engine and the prop. The electric motor could supply extra power during takeoff and function as a generator/dive brake on the prop during descent. In the event the gasoline engine failed, the prop/electric motor assembly could be declutched from the gasoline engine, providing you with temporary power to maneuver around and land safely. Gasoline engines in aircraft tend to be very reliable, but when they DO fail during take-off or landing, the most vulnerable parts of the flight, the results tend to be catastrophic. As such, the gasoline/electric hybrid would be of no use during cruise but it MIGHT improve the safety factor during the most vulnerable parts of the flight.