If you mean, do the legendary effects improve with leveling, I think the answer is no.
The weapon or armor with the legendary effect (dropped by a legendary foe) will have a random assortment of mods with the legendary effect added to it. The mods will be better as you level, though. You can still re-mod the legendary weapon or armor however you like, without endangering the legendary effect. Appears to be a randomly generated item with a random legendary effect. The damage of the weapon does not level. It is the better mods that result in the higher apparent damage. The damage of the un-modded weapon only levels if you add perks to the appropriate skill. (afik)
You can farm for what you want, though.
I found a legendary guy just inside a building, and repeatedly reloaded a save from just outside the building until he dropped a legendary sniper rifle. Then I repeatedly reloaded the "auto-save" that was created when I entered the building until the Legendary effect on the sniper rifle was the one I wanted. Instigator.
Read about doing this on some other website and decided to try it.
The legendary foe did not spawn 100% of the time, though, so it took quite a bit of reloads on the outside of the door to get the sniper rifle (not the pipe one, I wanted the hunting one).
edit: Then reloads of the auto-save to get the legendary effect I wanted.
May try for an exploding shotgun at some point if I don't stumble across one soon! 