It is possible to do, for each LED you would need to take a feed from the wiring for the LED in the center console. Connecting the wires and routing them through the doors so they don't snag or get caught in anything is the easy part, its the mounting of the LED's that will be hard, considering the stalks move and that movement quite sudden and comparatively "violent" when they move.
I'd recommend locktight hybrid glue, though this MUST be left for 24 hours before using in anger (kept my rear view mirror attached for the last 12 months so I highly recommend it), so the LED is less likely to fall out with continued use.
Or... Mount just ahead of the stalks through the door card, I've seen a few done like that as aftermarket mods and saves threading the wiring around the locking mechanism.