Yes, but for example with the "dying night" iconic weapon you can't just go from uncommon to legendary, you first need to upgrade to rare, then epic, and finally legendary.
To get components cheaper and easier to mass produce/farm I suggest to invest attribute points on technical ability, so you can level up your crafting, and also to activate the perks that gives/saves you more components.
To farm common/uncommon/rare components I suggest to get the "Uncommon Bounce Back MK.2" spec, so you can mass produce these and dismantle them:
To farm rare/epic components, get the "Epic CHAR Incendiary Grenade" spec:
To get cheaper legendary components, go to the ripperdoc Robert near the Kabuki market and buy the cheap "Legendary Beast Mode" crafting spec. If it's not available on the store, go outside, skip time 24 hours, and try again. Note you may need to do this a few times until it's available.