Doesn't the same rule apply (only more so) for FWD? If your rear wheels start to slip and you step on the gas, you transition weight off the front wheels, while simultaneously increasing the torque on them, making it more likely they'll spin? Honest question, I've never really pushed a FWD car on a track before, partly because their handling is just counter-intuitive to me.
If you're spinning out, it's because the rear tires lose traction when the front wheels still have it. If you shift weight off the front wheels, it has to go to the rear wheels, which although they may be sliding along the lateral axis, are not sliding along the direction of travel. Since they're rotating, adding weight (force) may cause them to cease sliding laterally since the friction will increase.
So yes, you're correct that the front wheels will start to slip. If you're cornering near the limit at a constant speed, adding throttle will cause your line through the corner to widen. Lifting the throttle will tighten it up.
Contrast this behavior with a RWD car, where if the rear tires are sliding laterally, adding throttle may cause them to slide in the direction of travel as well, completely breaking traction; while lifting the throttle may reduce the force on the tire in the direction of travel, allowing it to regain traction as it rotates. Lifting too much, however, can cause the drag of the engine and drivetrain to exert too much force in the other direction, causing "lift-throttle oversteer."
This means RWD cars potentially can exit a corner faster, because the weight transfer can add traction to the drive wheels, but too much causes a spin. In a FWD car, the weight transfer away from the drive wheels means too much throttle leads to oversteer. Safer, but potentially slower.
Racing FWD cars is fun, and probably demands less skill than RWD cars. The proper reaction to a spin is reversed, and catches a lot of people off guard. I think after 9 races I'm finally getting it.