You might be able to get away with it, but beware that a LED has a very low reverse voltage. Also beware that relatively high current pulses (300mA) will pass through the LED which could shorten its life.
It's hard to know how the LED will eventually fail, and whether that failure will cause other problems for you.
I wouldn't recommend it.
Any rectifier diode you can scavenge out of some broken piece of equipment will probably do far better.