Protonmail does not offer the possibility of using a email client (except using the beta bridge for premium users).
Right now Rambox or Franz offer Protonmail service app that are similar to the desktop version (like multiple accounts).

The dedicated desktop application could offer an alternative solution to email clients, like keeping a local readable copy for offline purpose, and eventually searching through local emails.
Because it may be a privacy concern, this feature could be either locally locked (local encryption?), or simply and opt-in (disabled by default).