Sockets and Conduits, yes. Upgrades past 220, no.
In the notes from Hotfixes July, 20th: “The new socket adding item, Alloy-Warping Facetor and conduit upgrade item, Death-Bound Shard should now be purchasable by all characters on your account from Archivist Roh-Suir once one character has reached Tier 6 Research.” It does not mention the 226/233 upgrades and since that’s tied to renown as well as Tier 6, it seems that’s unfortunately “working as intended.”
The person in THIS THREAD reached Tier 6 and thought for sure it was a bug that he couldn’t upgrade to 226/233 on his alts, but that doesn’t seem to be the case–it’s intentional.