I think it would depend on which side Hannover chooses during the Napoleonic Wars.
If it sides with France it will propably be annexed - or at least large parts of it, thus most likely shorten the time it took to unify Germany as Prussia would have access to its territories along the Rhine.
If it sides with the old powers it could become a counterweight to Prussia - perhaps even gaining some of the lands that Prussia got at the Vienna Congress - protected by France and Austria.
In that case, a war would most likely be neccessary to unify Germany - provided the 1848 revolution still fails.
If Prussia wins (which it could, even if Austria sides with Hannover) the unification could come a few years sooner than OTL. If Prussia looses the possibilities are endless

But even three German States (North - capital Hannover, South - capital Vienna and Prussia) are possible as the desire for a united Germany did exist among the people, so this "kleindeutsche lösung" seems logical as it would also deal with the difference in mentality in North and South Germany. This would be the peacefull solution.
I do not see Hannover agree to a Prussian King as Kaiser of Germany - as they sided with Austria in OTL during the 1866 war.