No. The amount of conventional current (not electron current) entering the base and flowing out through the emitter determines whether an NPN turns on (i.e. how much current passes from the collector to the emitter). For a PNP, it is the amount of conventional current flowing into the emitter and out of the base that determines how much current passes from the emitter to the collector). The base-emitter junction behaves like a diode which is where the typical 0.7V value across the base-emitter comes from.
Note that things like "the voltage on the base" have no meaning for a transistor. The voltage relative to what? Relative to ground? What if neither of the other two pins are at ground? Voltage is relative and the transistor does not know what the voltage is anywhere except between two of its pins.
Saying "the voltage at X pin" is like saying "the distance at your house". It doesn't mean anything.