Not really, no. Current doesn't flow through a MOSFET gate like it does in a BJT base.
In a NPN BJT, the current flows from the base to the emitter, and each little bit of current can pick up a much larger bit of current from the collector, allowing the whole thing to act like an amplifier. It gets tricky to keep right in your head if you think of electrons as the bits of current, since those flow in through the collector and out through the base and emitter, but as far as the conventional positive current model goes, it mostly works.
In a N-channel MOSFET, however, there is virtually no flow of current from the gate to the source, at least not until right before the magic smoke gets out. Instead, the gate is like a capacitor, collecting a charge imbalance relative to the source. When that imbalance is high (aka when the capacitor is full), current can flow from the drain to the source. When the imbalance is low, or negative, current can't flow.
PNP and P-channel are similar, but backwards.
Think of the base current as smugglers sneaking through the gate, while the gate charge is thugs scaring the guards away, without actually crossing themselves.