In short: You can, yes. It's almost exactly the same circuit. The only difference is that you need to connect a resistor between your logic pin and the transistor base. The value of this resistor depends upon your choice of transistor and the load current you are switching. Though current consumption is slightly higher for a BJT, the difference is negligible in almost all applications.
That said, there isn't really any advantage either. As a general rule, BJTs are used for analog purposes. Amplifiers, oscillators, that sort of thing. For simple digital switching, the FET rules.
It's very common to use a small, logic-level transistor (BJT or FET) driven off the microcontroller in conjunction with a pull-up resistor in order to control the gate voltage on a much larger power MOSFET for switching higher currents. It's cheap and reliable, though not usable at high frequencies.