A starter motor will generally spin the engine at nearly idle speed (pretty quick). A drill motor may or not be fast enough to be effective.
The amount of fuel actually used by the engine is very small. The bigger question is if the fuel pump is operational. If it's pulling fuel from the tank to the carb, you're good to go.
If the engine does not respond well to a couple of small drops of gasoline mix dropped in the spark plug hole, I would suspect your ignition system may not be functioning as designed - OR - the engine isn't being flipped/spun fast enough. Not being familiar with your power supply, I would be suspicious of that.
Flooding is obvious when pulling the plug after a few minutes of starting attempts. The internals of the plug will be soaked with fuel - very obvious.
Opposite is true of a fuel starved engine. That plug will be dry, with no signs of moisture.
Cracked components or leaking gaskets shouldn't prevent the engine from starting. They'll be more obvious when trying to get it running right.Often you will see fuel stains on the outside of the engine - which can lead you to finding items like that. Keep an eye on the engine early on.
It may pay you to seek out a replacement spark plug. NGK CM-6. The OEM plugs delivered with many engines have a spotty history. Some work great for quite a while, others are trouble right out of the box. For that reason, many are replaced with the NGK plug immediately.