If you are asking about the regular AppleCare warranty, that would not cover any kind of physical damage to the port, but it would cover a manufacturing defect.
Of course, if this were a manufacturing defect, the issue would likely have shown up long before now.
So, there is a real "gray" area here. All that you can do is make an appointment at the Apple Store or take the phone to an authorized Apple service shop to let them check out the phone and go over your options with you.
You can find a list of authorized shops in your area using this link:
Find Locations