will replacing the battery on a ipad that has been dead for years work to retrieve the files contained on there

Yes, but depending upon the age of the device the problem may be finding a battery. Obtaining service for your Apple product after an expired warranty - Apple Support

Were the files stored in iCloud too? If so, log into the iCloud service and see if they are still there. I have some in my account that are 5 years old.

If the battery has been fully discharged, all locally stored data will have been lost. Installing a new battery will also cause the filesystem to be fully reset.

If you have an iTunes backup, this can be restored to the iPad. Unless refreshed, an iCloud backup may have been automatically deleted.