TL DR:
If you take the Archmage Vault Quest but do other quests first glitches will appear (actived communication pool).
If you take the Arch Mages Vault Quest, but skip it and get the books of storm and do the Bekarna's Folly quest by chance first (I love driving around randomly and kill discover things), you can't just go to Arkemyr and talk to him. He is not in his study. He sometimes glitches in his labratory at the activate communication pool. Sometimes is just missing. You can use the pool and talk to the arch mage council and Arkemyr. The are talking about Bekarna's studies.
When Arkemyr is glitched in, you can talk him and he talks about the robbery of his vault (which did not happen yet). There is no way to cancel the quest to rob the Vault.
This is not the intended sequence of events, but this is how I played.