I don't believe it is really a good idea for a regular player to play a Ship's AI, fr the same reasons that Nashoba pointed out.
The Ship's AI is a GM or Co-GM position, as in many plots it can be important to said plot.
I think it should, however, be possible for a Ship's Avatar to be a PC, as those are part of the ship's AI system, but are somewhat disconnected from the ship itself, allowing them actual character interaction while still allowing them to serve several functions the AI is normally used for, such as giving directions, informing other characters about the ship's status, and relaying orders from the captain.
On the idea of actually making a ship itself into a PC, you also have the problem of needing to write up its crew, as a ship without a crew really isn't interesting, a lot of what makes space battles fun to read is the crew interactions going on inside the ship during battle.