Yes, the zipper pull can be repaired. It happened to me.
I just gave it to my SA (at NM) and she sent the bag out to fix.
I forget how long that took...maybe about 4-ish weeks.
It cost me about $100.-$150. Not too expensive and Chanel cleaned it too.(mine is the pale blue...almost white colored)
They sent my bag back to me directly to my home. Although I can't remember if I had to pay for that shipping. You'll have to ask the SA for that detail.
I suppose you can also have it fixed at a trusted shoe repair store. However, I wouldn't...for the price we paid, going to Chanel only makes sense.