It will show an error count if there are any differences in what is read from the parity disk and what is calculated from the data drives. The messaging is currently the same whether those errors are simply noted, or corrected.
Correct. Parity is kept up to date in realtime as writes are done. As long as the drive internal caches have finished their writes before power is lost, there should be no sync errors.
If there are writes in progress, the data drives are higher priority, so it's entirely possible that a write can be successfully completed on the data drive but the parity write has yet to be fully committed, causing a sync error, a correcting parity check will complete that process. It's also possible for a power cut to corrupt a data drive if a write in progress gets cut off at just the wrong moment. In that case parity can't help, because it will have even older data. Most of the time the file system checks can at least get back to a readable state, at the expense of a corrupted file or several.