atoms - Do hybrid orbitals exist in unbonded molecules? What would they look like?

For example, the ground state of a neutral carbon atom could be notated as:

$$ [\ce{He}] \underset{\ce{2s}}{[\uparrow \downarrow]} \underset{\ce{2p}}{[\uparrow \vert \uparrow \vert \; \;]} $$

I know $\ce{s}$ orbitals are shaped like spheres so the two electrons in the $\ce{s}$ orbital should probably form a spherical shape.

But how should the electrons in the $\ce{p}$ orbitals be distributed?

I think in the end result a neutral carbon atom is either shaped in a trigonal-planar arrangement or a linear arrangement.

So do hybrid orbitals exist in unbonded molecules? What would they look like?

I think this would have interesting results for collisions between atoms and how probable certain reactions are.