In Generation 1, the player will be unable to defeat the Channelers and reach the end of the Pokémon Tower if there are no available moves (with PP remaining) that can damage Ghost-type Pokémon, either directly or indirectly such as via confusion. This is due to the fact that in this generation, Ghost-type Pokémon are immune to Struggle (being a Normal-type move), all opposing Pokémon have infinite PP, and there are no moves or abilities that can ignore type immunities (Foresight, Odor Sleuth, etc.). This applies to the battle against Agatha at the Indigo Plateau as well.
Assuming that no moves are learned from TMs or from other games (Gens 1-2), which Pokemon in Gen 1 cannot learn any level up moves that can damage Ghost type Pokemon?
P.S.: I was watching MahDryBread's video of him attempting the challenge to beat Pokemon Red with only an Eevee. (link) He said that this challenge is impossible because he cannot damage any Ghost types at all and cannot progress past the Channelers and the Pokemon Tower.