Do electrons hybridize only during bonding?
To expand on orthocresol's excellent comment, you confusion likely comes from a common misconception. 


  Electrons and orbitals are not the same things. Electrons are fundamental particles with particle-wave duality. The behavior of electrons can be modeled with wavefunctions. Orbitals are mathematical constructs based on the probability density of the wavefunctions. 


Technically, orbitals do not hybridize because orbitals do not exist. Since orbitals are mathematical constructs, they do not correspond to any physically observable entity. Electrons are the physically observable entity. Electrons do not hybridize. Electrons interact quantum mechanically to form bonds when their wavefunctions have appropriately matching energy and symmetry. Electrons then adopt new wavefunctions for their new situation. These multielecton wavefunctions can be intractable. 

Hybridized orbitals represent a model that simplifies some of the mathematics by replacing the canonical hydrogenic atomic orbitals with hybridized atomic orbitals that are oriented in directions that match common molecular geometries. Orbital hybridization is a model that is thus only useful when describing bonding. If there is no bonding, hybrid orbitals are a nonsensical model.