It shouldn't be. It's 1/16th of a chunk. Its movement won't be simulated, and when it gets picked up as an item, the room remains loaded in memory but the doors are shut so it can't send items or blocks in or out of the room. When you place it, there should be a brief (split second) lag spike as the game writes up a translation set that tells it where to teleport objects or blocks when they move across the boundary into or out of the room. If a large number of players placed these near each other it could get laggy, but it would take probably dozens all in the same vicinity, all with laggy projects going on inside. There's other ways to lag the game, you don't need rooms that are bigger on the inside to make it happen.
You only get one portable room, it's attached to your character and not the block. Probably shulker boxes won't be able to hold portable rooms, just like they aren't able to hold other shulker boxes. But you can put shulker boxes in your portable room.
You also can't place a portable room inside someone else's portable room, the main reason being that you might never get it back. You can get multiple portable room inventory items but you can only have one placed in the world at a time. Because of this, it must be placed in one of the three main dimensions, to ensure you can always get back to it and pick it up if you need to move it.
I can already hear the din in my head!
Okay... It seems like you have a good idea, but I don't think it's the best solution to the problem this suggestion is trying to fix.
However, I might support this suggestion if you opened up a seperate post for it... I'd be able to have my own personal TARDIS in Minecraft! (Minus Space/Time Travel, a lot of the room inside it, and a lot more features, but it would be cool to have a personal dimension for whatever purpose.)
I get offtopic a lot, be warned. I also often mention a Minecraft clone called Minetest. The clone is nowhere near playable with it's default game in my opinion, but it's at least the start of a good open-source voxel rendering engine, and maybe one day it might be decently playable.