High chance of it not working. If you go to VFS with Tatkal and renewal selected and if they see your binding is off, they will ask you to refile in damaged passport category. Which is okay, you can fill in a new form right there. So if you want to be safe than sorry and have time then just apply for damaged category or prepare to do that when you reach VFS office.
My experience was as below for above situation (in USA):
I already submitted online application for my passport renewal before I sent the physical application. Then I realized that my passport’s cover binding got separated. So I did not send the application just to make sure that it won’t be refused and I reached out to customer service and they said I need to file under damaged passport category. I submitted the new application and sent the physical documents again. It got approved and received passport within 3 weeks.