I think the answer is a definite yes but that doesn't mean that he's out of the woods by any measure.
Lets say you can measure how well a person is doing quantitatively (Its not possible of course but lets assume.)
Lets say the standard for "doing okay" is about 50. Anything higher is doing very well anything lower, not so much.
If we were to measure Chris on this "doing well" meter he has jumped a good 10 or even 20 slots since the death of Bob. And a few spots higher since the blarms fuckery. He's attempting to socialize, he's shut the fuck up about blarms, he's no longer talking about how depressed and sad and lonely and steel heart he is, which would lead one to assume hes no longer depressed like he once as, and most surprisingly he has managed to make a surprisng amount of money off of Sonichu. He is also now creating art on the regular basis which is a good way to not be fucking depressed. These are all objective facts that we can all see.
The problem, I think, some of us have with saying he is getting better is that when we were first introduced to Chris he was starting at like a 3 and slid down to about a -50 at certain points. So yes, he's getting better but right about now hes like at a 10. There is still a shit ton wrong with his life. His hygiene still seems questionable, his house is still filthy, his dogs sound like they were in the Vietnam war, he still has a less than healthy relationship with his mother, and his dating prospects are less than zero. And this is setting aside issues that are up for debate like his alleged transgenderism and whether or not he is or can make genuine social connections at the gay bar.
But the TL;DR answer to me is a resounding and easy "Yes." he is getting better. It may all go to shit tomorrow and the work isn't even close to done but he is doing better. Especially when you compare him to like ADF or something. Shit ain't all that bad, right now.