Probably will take more than a couple of eyedroppers (of course that depends on the size of the eyedropper).
When you turn off the engine, with modern fuel, you will get some perculation of fuel into the throttle area. The lower side of the plugs are exposed to the throttle area, and can thus seem wet.
You may have a problem; you may not. Always best to do a little testing before repairing.
Two schools of thought:
(1) If it ain't broke, don't fix it. (2) If it ain't broke, fix it until it breaks.
Jon.
Good carburetion is fuelish hot air Owner, The Carburetor Shop LLC