It works either way, depending on what you want to do. You can, if you want, charge the cap through the LED. If you don't first discharge the cap, no current will flow once it's charged. If you set it up so it discharges in 10 usec, but charges for 10 msec (extreme case, but you get the idea), you can go along and discharge lots of caps during that charge time. It involves more parts and more thought, but it allows you more freedom.

Once upon a time, we used to drive stepping motors that way, too. It helps control heating in cases where, due to some anomaly, you may lose control due to a power hit.

RE