Each covalent bonds contains two electrons, so, when a covalent undergoes homolytic clevage, each fragment receives an electron from the former bond. In other words, the electrons from the former bond are shared equally among the fragments, leaving each fragment with an unpaired electron and therefore creating a radical.
As far as your question as to whether coordinate covalent bonds can undergo homolytic cleavage, I cannot think of a common example. I would imagine (but I have a active imagination) that there are some examples in organo-transition metal chemistry, because it may be possible to stabilize a ligand complex by performing a one-electron reduction on a multiple bond. However, this is pure speculation on my part.