No it could not (short answer).
Long answer - if an airplane (e.g. BE200 King Air, etc.) was sitting in hurricane force tailwinds with the power levers moved to beta/reverse range, all this would do is create thrust in the opposite direction that it was designed to fly in. It may generate more reverse thrust as more air is forced through the propeller disks than at low forward speeds. Note as well that beta and reverse power lever positions do not increase the engine power output to its maximum flat rate value, which, while useful in slowing the aircraft during landing ground roll, hamstrings its ability to takeoff.
An airplane like a King Air has a liftoff speed around 100 KIAS. To obtain this airspeed in 100-115 mph tailwinds would require a ground speed of 190-200 knots. Typically, accounting for wheel friction and ground covered during acceleration, this typically requires an increase in ground roll of around 10% for every 2 knots of tailwind over an airport surface*. In this situation, a 100 mph (88 kt) tailwind would increase the ground roll by approximately 440%. This means if the airplane has a ground roll of 1,800 feet in still air, it now needs 9,720 ft to obtain Vr in! Unless you’re departing from at airport with a VERY long runway eg KLAX, KATL, ETC, the airplane will never get airborne, overrun the departure end and impact terrain at a very high speed with a high risk of total destruction and loss of life.
Lifting off from a heavy tailwind is also impossible as the airplane is not structurally nor dynamically stable to fly with a relative wind from behind. It would quickly depart from controlled flight shortly after liftoff and impact terrain. End result is not good here, either. And even if you could, in theory get it to fly in these conditions, you now face the challenge of reversing this condition for forward flight.
Bottom line is, if you were to attempt a takeoff in 100 mph winds (and this, too, is extremely dangerous), you would be advised to taxi to the opposite end of the runway and just attempt a headwind takeoff. The airplane could become airborne very quickly here with a minimum of risk.
*Illustrative purposes only; do not attempt to use for flight operations without consulting manufacturer approved performance tables for airplane in question.