Updating an item's barcode will not affect its checkout history or statistics. Each item in Koha has a corresponding itemnumber, a persistent, unique identifier in the database. That itemnumber is what populates data in reports, including in tables like the statistics table, issues/old_issues tables (checkouts and checkout history), or the reserves/old_reserves tables (holds and hold history), to name some of the most common few tables for circulation reporting.
Practically speaking, this means that if a barcode sticker comes off an item and the library needs to replace it, all the history of that item is tied to its itemnumber, not the individual barcode. The only limitation is that the new barcode cannot be a duplicate of any other barcode already in the system.
What Happens to the Statistics of a Deleted Branch?
Koha has guard rails around deleting important information like a branch code if it is in use, but once a branch's items are all transferred to a new location and no patron accounts remain using that branchcode, the branch can safely be deleted from Koha.
Statistics capture a snapshot of information at time of transaction, so the statistics.branchcode field of statistics reports will still retain the branchcode for historical circulation counts, even if the branch has been deleted. Statistics reports linking out to additional tables may need some adjustment in light of a deleted branch, but the statistics do still remain and can be reported on.