It does not appear to have been so. Reading <PERSON> Business Insider article, It Took <PERSON> About 27 Seconds To Decide To Be In 'Birdman':
During a panel at New York Comic Con for the film, <PERSON> shared the story of how he was cast in director <PERSON> movie about a washed-up actor, <PERSON> (<PERSON>), hoping to rejuvenate his career with a Broadway play.
<PERSON> said he first learned about "Birdman" while filming another movie, which he flew home in the middle of shooting to discuss.
"I got a call saying, '<PERSON> was making a movie,'" said <PERSON>. "I was working on a movie and they said, 'well, unfortunately, you probably can't fly home because you're in the middle of making this movie' and when his name was mentioned, I said, 'Well, maybe I should find a way to fly home because, like I'm sure <PERSON>], I'm a big, big fan of his movies."
The actor said it took him less than 30 seconds to decide to star in the movie after dinner with <PERSON> who has made movies including "Babel" and "21 Grams."
"So, it was that simple. I flew home and they wouldn't ... they couldn't tell me what it was about and now that I've done the movie I understand why they couldn't explain it because I'm not sure what happened," he said.
"I went and had a dinner with him [<PERSON>] and it was very pleasant and very interesting," <PERSON> said. 26
"If you've ever spoken with him, you'd know why. He's just a very interesting, extremely passionate guy which is contagious. At the end of the evening he said, 'Well, here. Read this.' It took me about, I don't know, 27 seconds to decide, 'Yeah, I want to do this.'"
If it had been specifically 'written with <PERSON> in mind', he would have been actively courted. If this article (and <PERSON> himself) is to be believed, he dined with <PERSON> and only then was given the script to read and accepted it. Had it been written 'for him', it seems more likely that they'd have contacted <PERSON> (or his agent) directly, and he'd have been in on it from the beginning. 417