It is not a secret as we all know from official plot details and The Wrap's interview that Depp character's brain is gonna end up somehow in computer.
Knowing this, after reading the script I can see how Wally could make it a short shoot for J. Depp. I suspect much of it will be Depp in front of green screens. As for where is he, how he looks like and other - the vfx guys will have much fun, I think!
But he owned those 13 minutes. I can't see Depp own such a simple role And also:
Depp is gonna be playing a computer for majority of the film.
You are underestimating his presence, BIG SPOILERS, those who haven't read the script, resist.
He will be hologram and I think they will go Crowe's Jor-El way, his hologram will be real and not computerized otherwise it makes no sense whatsoever to pay the man over 20 million for such a small role.
I think the most fascinating aspect of his character that seems to be hinted at in the trailer is that he becomes thirsty for this immortality/source of power from the network of all the computers of the world. Kind of like a Vampire in the world of the megabytes and computer code.