Im not sure of kelp. However, when a salt system is up and running the sump is often seeded with a wad of chaeto or other seaweeds. It promotes the reduction of phosphates in a salt system. So, the answer to the question is "yes", about seaweed being kept in a tank.
Kelp needs very intense lighting in order to grow. They also grow too large for an average home aquarium but there are smaller species that will stay small.
There are many other macro algae or seaweed that can easily be kept in an aquarium other than kelp.