Interesting. The Bloatmage cannot digest the immortal ichor as he could digest the blood of other creatures - the immortal ichor is immune to acid and to bludgeoning. A GM could nonetheless decide that the Bloatmage's Absorb Bloodline ability is beyond physical (Archives of Nethys doesn't state whether Absorb Bloodline is a supernatural or extraordinary ability and I don't own the sourcebook).
Assuming that Absorb Bloodline is a supernatural ability and the GM allows it to function, then the Bloatmage gains appropriate bloodline powers. As a default choice for 'evil deity' I would probably plump for Infernal, Abyssal or Daemon bloodlines. Possessed bloodline might be an interesting choice. If the Immortal Ichor isn't actually dead when the Bloatmage drinks some of it (an unlikely scenario) I would definitely call for an Ego struggle, as though the Ichor were an intelligent weapon contesting with the Bloatmage. I might do that even if the Ichor is dead when consumed. Perhaps I might give the Bloatmage flashes of the memory of the Ichor, and steer him towards attempts to revive the dead deity.
I see lots of opportunities for campaign plot development.