I've been homeless, so perhaps you'll forgive me for being biased against thinking like that.
I would never class mental illness as a choice, or of poor decisions whilst someone is suffering mental illness as a choice.
It sounds to me a lot like victim blaming. That a person may "choose" to be homeless because they have mental illness... isn't that more like a lack of compassion by fellow citizens to help support those who are suffering from mental illness?
Would it be different if it were a physical illness? That man is homeless because he chose to be due to having a broken leg. That sounds ridiculous, and frankly that's how your statement sounds to me.
I "chose" to be homeless. Sure, my choice. I could've stayed in a violent and sexually abusive environment and living in poverty. But instead it was my "choice" to sleep on the streets to escape it.
I didn't even choose hostels - I voluntarily declined a bed to sleep in - because when you've come from a shared sleeping environment in which you were not safe and feared physical abuse nightly, then you may understand my reticence to enter a shared sleeping environment with strangers, some of whom as you pointed out may have mental illness.
Perhaps this is all just a mental construct to make you feel better about yourself. If you are able to imagine that these people took responsibility for themselves and this was a free choice, you are able to absolve yourself of any individual part of the responsibility to show compassion and empathy towards fellow humans.
If all we've got to offer people as a society, is a "choice" to sleep without shelter, without warmth, without safety... I'm not really seeing how anyone can say that people "choose" this.
Edit: Whilst this issue has attention: http://crackandcider.com/ I'd urge anyone doing secret santa's, or just feeling flush to go there, and buy things for homeless people. They're good people, taking no profit but covering costs, and just giving this stuff to people who need it.