Ive seen it and no I didnt see any connection to being DID.

if I remember right and not mistaking the film for another one the plot line is that Tommy had PTSD from seeing his step father kill his father, then his mother and his step father take Tommy through all kinds of medical, mental and religious treatments hoping for a cure, at some point Tommy is left in care of a relative who abuses him. when tommy looked in the mirror his "ID"appeared to him..

here where I live and work the Id, Ego and Super Ego are not considered alternate personalities..

the mental health community here where I live and work believe every person mental disordered and not have an "id" "ego" and "superego"

the "id" is a persons instincts... example when you put your finger on something hot your brain sends a message to your finger to pull away from the burning object..

the ego is also something every human being has... the brains ability to think logically and realistically...

examples

knowing whats real and whats not real
being able do math and other logical reasoning thinking

the superego is a human beings ability to have morals, critical thinking

example
knowing right from wrong,
having a conscience, regretting bad behaviors. ....
being able to think ..gosh that was dumb or wow I did good that time type self talk..

here where I live and work the mental health community believe DID is two or more alternate personalities that take control of the body and function as a separate being living life with their own way of being.

Example I dont like tight clothing, bars, drinking and smoking, my alternate personality would dress up in tight jeans and sexy shirt, go hang out at bars, drink, smoke and pick up intimate partners.

but I do understand what you are saying.. people can find all kinds of things that are not meant to be in movies and books... one of my favorite songs is about a divorce but if I am in a mood where Im focused on my DID symptoms the words can sometimes sound like they are talking about DID stuff not two people getting a divorce and their feelings that go on through out the process of getting their divorce...

I have a friend who swears the sound of music musical is about the nanny having bipolar disorder and schizophrenia when I say its about one family adjusting / transitioning and gaining freedom during the occupation by the nazi's..

people can read anything into anything... so I can see your point even though to me the movie said something different.