I've made it to level 100 on lockpicking, but I have not attributed any skill points whatsoever to the skill. If I make it legendary, I know that it will reset my lockpicking to 15, but will I get any skill points out of it?
No, you will not get any extra points out of it by resetting it. You will only get the skill points back from the perks you have used skill points for, at a 1 to 1 return rate, thus no skill points will be gained or lost, just returned.
The ability to level it back up to 100 will allow you to level your character up, however, which will give you more skill points.