I think it would be hard to use a Chanel as a diaper bag as well. As others have mentioned, they're not really meant for it and I'd have a heart attack if it got misshapen or stained.
That said, I did try to use an LV Neverfull as a diaper bag myself. I had an MM size and it was ok, used it with a purse organizer inside (Purse to go) so just in case something did leak, at least there would be some barrier between the spill and my purse lining. However, I did end up just getting a regular diaper bag to use because I realized that when I had the bag loaded up, I really didn't want to carry it anyways because it's too heavy so it would sit underneath the stroller. And if you're not even carrying the bag, then who cares what it is?
Currently I just use the big diaper bag when we're going to be out all day, and I carry my own smaller purse. If we have the stroller, then the daiper bag goes on the stroller, and I carry my bag. If we're just running out for a quick errand or dinner, then I just stick a diaper, wipes, and couple essentials inside my small purse and don't bring a diaper bag. I usually use my LV Favorite MM when I'm out with the little one because it's cross-body, light, and hands free but still large enough for my stuff and a few baby essentials. I also have a neverull GM now, which I like better but again, if you're going to be holding the baby and carrying a big bag, it gets really heavy.
I wouldn't use a Chanel when I have the baby with me because sometimes she'll kick the bag while I'm holding her. It's fine for my LVs, they can take it, but I wouldn't want my Chanel getting kicked or stepped on.
Hope that helps!