Humn,
looking at the dimensions it would appear you should be able to get some kind of LED package and driver into the can, however having a look at some Google pics of the light it may end up being a one shot deal with fitting them as i can see no way of getting them back out.
Currently the bulb is held in with a cir-clip and the power switch is external to the lamp housing? Correct me if i’m wrong, what I’ve written next won’t make any sense if i am.
If you press a module into the housing past the ridge to secure it with the cir-clip you would have no way of getting it back out again and you have no switch or power connector to remove at the back of the lamp to push the LED package out.
The other aspect to all of this is that it is so cheap for Chinese head units it may make more financial sense to buy a new head unit and wire it to the lupine battery.