Is an SN1 reaction possible in halobenzene?
Yes, that reaction occurs, but generation of the phenyl carbocation was much more difficult than anyone might have guessed. Here is a drawing of the phenyl carbocation.
First note that the 6 p orbitals making up the aromatic pi system are all still intact and overlapping - the aromatic nature of the benzene ring has not been tampered with.  Then notice that the cationic center exists as an empty $\ce{sp^2}$ orbital where the 



$\ce{C-H}$ bond used to be. The empty (cationic) $\ce{sp^2}$ orbital is orthogonal to the aromatic pi system; as a consequence there is no resonance interaction or stabilization of any sort between the two systems.  Further, being constrained by the 6-membered ring, the cationic $\ce{sp^2}$ orbital cannot rehybridize.  This results in considerable (low energy) s-character being used to stabilize an empty orbital, and is not available to stabilize other orbitals that do contain electrons! The vinylic carbocation, the ethylenic analogue of the phenyl cation, is much more stable and common (it can even be observed by nmr) because it is not constrained by a ring and can rehybridrize, thereby lowering its energy. It is both this total lack of stabilization and relatively high (higher than need be if rehybridization could occur) energy of the molecule that has made the phenyl carbocation such an elusive target.  

To stack the deck in their favor, investigators have run experiments using extremely good leaving groups such as nitrogen and the triflate anion. Magic acid and its variations, a very powerful acid that stabilizes carbocations, was often employed as well.  The nitrogen leaving group route, using thermal decomposition of aryl diazonium cations has been one of the few methods that has allowed access to this transient intermediate.

A few references if anyone would like to read more:


On Attempts at Solvolytic Generation of Aryl Cations - 1976
Attempts at Solvolytic Generation of Phenyl Cations - 2004
A one paragraph review - 2000