Yes, that will work. I'm guessing you have the v2 board (no D3). Just don't try cramming a diode with fat wires like 1N4004 or 1N5817 into the socket.
LEDs will give a louder, fatter sound. I used green LEDs in mine because that's the TS color theme. That and they have a higher Vf than red LEDs. Mismatched diodes will make even-order harmonics, which has a warmer, richer sound. If you end up finding combinations that you like, you can install a DPDT toggle switch on the front panel and wire it to the board.
The TS is ripe for mods, most of them are simply changing component values.
Or you could build a Frost Drive. It does everything an LGSM does and then some. Some of my Frost Drive mods can be applied to the LGSM.
Loving this pedal so far, definately one for the board. I have been playing with waterslide decals to try to improve the look of my pedals. Usually i finish it and have it sitting in the enclosure for a while before I'd put some sticker decals on it. Did this one first this time, and as you ahve...