Do you think a well built Cleric could solo the Carrion Crown Haunting of Harrowstone?

[Player III]

Minor spoilers follow:

I am currently playing through this adventure path with a group of friends, and all is running smoothly. The party gets along great, the story is quick and enthralling, all is well. The party only has two sources of positive energy in the forms of a Cleric and a Witch, which, I was slightly concerned about at first, but I quickly found the clerics channel ability and positive damage output puts down most haunts and undead in one or two spells. While not game breaking or anything, as she also needs to heal her allies whom are particularly not incorporeal like most everything they encounter thus provides excellent meat cushions for pretty much everything and the HP of the enemies does increase with CR along with limited spells per day means the party still needs to take breaks on a fairly regular basis. But this got me thinking, could you play this campaign solo with a well built Cleric and hold your own? I think the only real issues would be a few of the haunts and ghosts that can particularly mess you up if you fail some saves.
With the right feats and equipment, even from starting equipment, you would be a force to be reckoned with.

[Realmwalker]

Even with a Cleric in the groupr:

The Furnace, and Iron Maiden haunts damn near killed multiple party members. So even with a divine channeler they can be very dangerous.

[hogarth]

I haven't finished the adventure yet, but based on what I've played so far you might be able to, but it would involve a lot of tediously finishing one or two encounters and then running away to recuperate.

[Player III]

Realmwalker wrote:

** spoiler omitted **

Tomorrow is the day my party will run into the iron maiden, and they should have Father Charlatan following them at the same time, as well. It will be interesting.

But that furnace, man. My group beelined it straight into that room at level one.
They only barely managed to take it down, but not before it lashed and very much overkilled the summon their summoner had out. Needless to say, "it takes 16 damage" it not a nice thing too hear when the highest HP total in the party is 10.

[Mirrel the Marvelous]

My Undead Lord Cleric turned that adventure into a cakewalk. Grabbed the Undead Master feat (treats your cleric level as +4 when commanding or animating undead) so I had my own personal army that only seemed to get stronger with each encounter.