In Arizona, Maricopa county (at least) will send an email or text when a mailed or dropped off ballot is received, verified, and counted.* You do have to sign up with your contact info.
*Ballots received up through Sunday evening are counted, but the results not made public, before election day. Ballots received on Monday and election day are processed on Wednesday. Ballots received after the polls close on election day are discarded.