The TouchID button is an electro-optical sensor.
While the button and its sapphire crystal surface is robust, if damaged, the TouchID sensor will not be able to optically read ridge detail of your fingerprint. If damaged, the sensor must be replaced. Damage of this nature is very rarely reported within the Apple Support Community.
Your iPad may be repaired under warranty. Apple will visually assess your iPad and the button for any signs of physical damage. If none are found, a warranty claim will very likely succeed.
If you accepted the offer of the optional AppleCare+ plan when you purchased your iPad (or within 60-days thereafter), the repair cost will be covered regardless of cause.
You would be well advised to visit the Genius Bar at your local Apple Store or Apple Authorised Service Provider (AASP) - where the technicians will be able to assess your iPad - and you can explore your available options:
Genius Bar Reservation and Apple Support Options - Apple
Alternatively, you might use Apple’s mail-in repair service:
iPad Repair & Service - Apple Support
In the circumstances, you might be best advised to explore warranty considerations at the Genius Bar - that, with with abundant courtesy and a smile, you can talk to 🙂
