The short and sweet of it is, immortality and evolution are contradictory.
Evolution requires that the species genetically evolves and then the new replaces the old, through reproduction and death. That is, the new evolved genetic organism replaces the former.
For immortality to be consistent with evolution requires that the individual cells making up the organism themselves mutate, and all new cells that reproduce are made of the new genetic material. However, then these genes have to migrate to every other gene in the organism, or the organism becomes a compilation of many cells that each have a different genetic makeup.
Think in terms of the human body that is made up of hundreds of bacteria, each with its own genetic makeup, working in symbiosis. The mitochondria in our cells, for instance, are actually a separate organism with its own genetic DNA.
So, maybe, if you build the 'intelligence' into symbiotic organisms within the corporate overall body that is immortal, and these sub-organisms can themselves mutate over time, you have a chance at evolving intelligence in a unified corporate body encasing sub-units.
That is, in an extreme way, think of the brain of the organism as a separate entity with its own unique genetic code, that reproduces and dies off, within the overall structure of the gecko. Therefore, the brain can evolve as it dies off and reproduces, even though the body is immortal.
The problem is, every new 'brain' would loose the experiences and knowledge of the old brain, and would have to start all over again. Mind you, this is not necessarily a bad thing. The human mind has a finite storage capacity for new knowledge, memory, and experiences. Replacing it with a new mind every two hundred years or so may not be a bad thing.