I feel like this question hasn't been talked about a lot lately and I really must know. When I see the Imperial city all I can think of is going inside and exploring it. I have also wondered about places like Cloud Ruler Temple (I can't find a way in). I have tried to Google lots of my questions and asked while in game, but nothing seemed to have my answer.
The short answer: Not yet.
The long answer: While I'm not sure about the Cloud Ruler Temple, the Imperial City will definitely be accessible some time later this year (if everything goes as expected).
Just today ZOS posted a new The Road Ahead article by Matt Firor which includes a list of content that is planned or in the works but doesn't have a specific release date or schedule yet (emphasis mine):
- A system that allows grouped players to see each other even when they’re in different phases
- A justice system—steal from and kill NPCs and deal with the consequences if you are caught
- Migration of European Megaserver to our European datacenter.
- Field of View (FOV) adjustment
- Armor dyeing and tinting
- Two new Veteran Dungeons: Crypt of Hearts and City of Ash
- New region of Craglorn with a new Trial (the Serpent)
- Increased ability to pick up items in the world
- Thieves Guild and Dark Brotherhood storyline and quests.
- Horse Racing
- Dragonstar Arena—similar to Trials, but built for a group of four
- Improvements to fishing
- Crafting system improvements
- Improved Looking for Group system
- Better NPC facial animations
- Guild functionality updates: guild store interface updates, customizable guild insignias, tabards, and guild ranks, and Guild Kiosks—guild stores open to everyone that are available to the highest-bidding guild.
- Auto-leveling dungeons that level to your group leader
- Awards when you repeat dungeons
- Imperial City PvP dungeon
In case you're not sure what a PvP dungeon might look like, you should have a look at Dark Age of Camelot and it's PvP dungeon Darkness Falls.
In short: This is a big dungeon with opportunities to level and loot NSCs. However, other realms/alliances might enter the dungeon as well (it's an unlimited PvP area similar to DAoC's frontiers or ESO's Cyrodiil).
In DAoC access to Darkness Falls is limited and determined by the PvP success of one faction. So there's some added benefit by controlling a bigger chunk of the map and also some added risk: Do you leave the dungeon once enemies invade it or do you stick to it, gain more XP and possibly encounter some PvP? You could even try to fight back invaders, which is something I really loved doing on my stealth character (so there's been the limited ability to pick fights).
Keep in mind that the term PvP Dungeon in Imperial City PvP Dungeon doesn't necessarily mean that this is underground only. It's just some area isolated from its surroundings (i.e. Cyrodiil).