I have trouble writing a non-developing character for more than a few pages, and I imagine I'd have trouble reading one as well.

That said, anything that you can think of can probably be done.

I still have trouble imagining a character without a single trait or flaw though. Any writer attempting this would take on the huge risk of making their characters boring, unlikable, unrelatable, and forgettable. Its not a guarantee of failure, and a writer capable of penning experimental classics could probably manage to not make his readers fall asleep, but you're asking strangers on the internet to help you write you're novel. I could be insane. I could be eleven. I could be a dog, and if you like my advice, you'll take it. You're not the next Pynchon. Sorry to tell you.

Here's why this is generally a bad idea.

It's a common piece of advice to introduce at least one character in your opening sentence. Not every successful book follows this advice ("It was the best of times; it was the worst of times"), but a lot of them do.

Call me Ishmael.

Stately plump Buck Mulligan came from the stairhead, bearing a bowl of lather on which a mirror and a razor lay crossed.

I am an invisible man.

Lolita, light of my life, fire of my loins.

You don't know about me without you have read a book by the name of The Adventures of Tom Sawyer; but that ain't no matter.

See what I mean? It's a good practice. Anyway, you should at least introduce one character within you're first paragraph, but even then, it's not a rule. In fact, you can practically do whatever you want for the first 4000 words. That's how much a quick reader can read in ten to twelve minutes. Past that time, if you haven't hooked your reader, they will put down your book forever. Life is too short to read bad books.