Yeap, Alec. I was thinking of removing it, but then again .. The path would be Plus 5V, load, Rb, VBE, Ground (supposing that the LED has been moved to the collector side) .. Which doesn't arrange things, as the current that flows through the load is the same as IB which is small. I forgot it there.
I think that, BJTs being current controlled and not voltage controlled as FETs, either there would still be some current flowing through RB in that configuration... BUT.. One of the reasons I wanted to move the LED up to the connector instead of letting it in the Emitter, is that for the transistor to conduct, although being current controlled, its Base voltage needs to be slightly higher than its Emitter voltage (about .7v higher). If I left the LED there, the voltage at the Emitter with the LED lighting would be about 2.5 volts (for a green LED, I think I'm not mistaken..) so the Base voltage would need to be at least 3.2 volts. Moving the LED simplifies this a bit.
So, having that in mind .. What do think about adding a resistor instead of the wire, so that to keep the Base voltage higher than the Emitter voltage ? (The LED being on the Collector side).
We'd need to figure out how much current the load draws to calculate that resistor, in order to know which value would cause full saturation for the transistor.
Maybe even a diode that can withstand the load current, but cause a convenient voltage drop. Or a Zener diode .. How does it look ?