If nobody wishes to nominate and serve on an Executive Committee (E/C) then either the Owners Corporation (O/C) must assume its role thereby requiring General Meetings to make decisions that would otherwise be delegated to an E/C, or the O/C can resolve to delegate the E/C functions to its Strata Manager and to detail those in the Strata Management Agency Agreement.
Whilst there’s a prescribed maximum number of persons who can serve on an E/C there’s no minimum, so YES, one person (with a lot of spare time) accepting a nomination and a position as an E/C Member could take-on the roles of Chair, Secretary, and Treasurer.