It will work but I would use a bipolar transistor in this circuit. My reasoning is that to use the MOSFET as a switch its gate voltage needs raising more than knee voltage above the source pin. In a follower circuit like that, the gate therefore has to be at least 2V higher than the voltage dropped in R1 and the LED.
If you use an NPN bipolar transistor the voltage will only have to be about 0.6V higher. You can utilize the current gain of the transistor without needing so much drive voltage.
You could also consider reversing the operation, connecting the left side of R3 directly to 5V and using a PNP transistor with it's collector to ground as a shunt across C1.
Ignore the wiring resistance, it contributes only about 0.1% to the LED current drop.
Brian.