The film inception isn't really about dream sharing, and while your question asks if it's possible I think that part is mostly fiction. While we might be able to one day visualize dreams on a monitor while they happen, transferring and connecting two or more people to a host's dream is purely science fiction.
Still, the film is about planting ideas via one's dream. Using their subconscious to control their waking behavior. That part of the film is very plausible.
There are many psychology tests that measure's a persons ability to recall information from memory. When it comes to recalling information after a long period (several days) this is greatly improved if the information is studied just before a REM sleep cycle. If the person studies the information, sleeps and fails to dream, then recall performance is reduced.
There is a connection between the development of long term memories and dreaming. Which raises the question, can you introduce new memories during a dream cycle? Yes, I think you can or at least it's a very popular myth.
More info here: http://dreamscience.org/idx_science_of_dreaming_section-1.htm
So to answer your question, the plot of the film is plausible, the technique used in the film is not.