Its possible--in fact, its pretty much what Partybot was designed for.
The big problem with it, is I've yet to find a CC that's smart enough to 'get out of the red/black/blue/green stuff'. They also don't know to 'stop dps' when bosses cast certain spells, or autonomously CC on the initial pull. All of this is beyond the capabilities of the framework Honobuddy provides to CCs.
As such, you have to choose the instances you run very carefully. I've done Blackrock Caverns with it--full party-of-five was mine. I was unable to complete the Throne of Tides with the same party. (3rd boss with the mind control, black stuff on the floor was too much). These are the two lowest level Cataclysm dungeons, and both were non-heroic. The party gear was purchased blues from the AH and about 7500 gearscore.
I've had limited experience with Partybot and level 85 instances (which is what you want, I assume). As such, will leave it to others to provide the necessary hints.