Could Jeff Flake(R-AZ) run for the McCain seat in 2018 like Kent Conrad(D-ND) did in 1992?

Kent Conrad who was first elected to the US Senate in 1986 decided not to seek re-election in 1992. But when the other ND US Senator Quentin Burdick died in September of 1992, Conrad ran for that seat and won.
If McCain dies after the Arizona primaries which takes place on August 28, 2018, and a Special Primary Election takes place in late September/Early October. Flake should follow Kent Conrad's lead and occupy 2 US Senate seats in the same year.