Is battery replacement covered in the warranty?

Depends on the issue. If it's swelling during the warranty period absolutely.

The nominal rating is that it should be at about 80% after 500 cycles. If you manage to get in 500 cycles (kind of difficult to do in a year) then the battery won't be covered under warranty simply for losing capacity. If it's under 500 cycles and under 80% battery health, that's a good case for a warranty replacement.

Batteries - Service and Recycling - Apple

iPhone Owners

Your battery is designed to retain up to 80% of its original capacity at 500 complete charge cycles. The one-year warranty includes service coverage for a defective battery. If it is out of warranty, Apple offers a battery service. Prices and terms may vary.

If the phone is within the warranty period and the battery health is below 80%, yes.