If I recall, he's the one who left, you didn't throw him out. He also took half the money in the joint account, so he's got an option to not be broke, either.
I think him being homeless, and having a hard time of it, is a good lesson on the consequences of his own choices and actions, and letting him back in would be codependent at this point.
I do agree with Babyblue, whether an action is codependent or not has a lot to do with a lot of factors specific to the situation, and a lot of the individual's reasons.
Example: My parents will be sleeping overnight at my apartment the Friday of Memorial Day weekend, because they're too cheap to get a hotel, and they don't want to deal with the bugs while camping. I don't have a good relationship with my parents, I really am not comfortable with them staying overnight in my apartment.
If the facts stopped there, that's a very codependent thing to do.
Add to that, we're going to an airshow the next day, I really want my two little brothers to go with me, and having my parents and my little brothers spend the night at my apartment is the only way that will happen, so it's a decision I made so that I can also get what I want. I will be staying in my bed, and everyone else will sleep in sleeping bags on the floor (my parents are bringing them), unless my little brothers want to sleep in my lumpy sofabed. Plus I'm curious to see what my kitten will do, with all these additional people sleeping over.
With those facts in place, it's no longer codependent. It's a compromise.