No, There is no End point to any part of the game. You could play the cell stage with the same creature for years, so long as you do not click to evolve it would never end. no number of deaths or time taken ends it. Its the same for all the phases of the game.
Tribal, Civ, space, can all be played as long as you like, all depending on when you decide to hit the advance button.
Depending on how you look at the game , you could rationalize that beating the game would be reaching the center of the galaxy, finding Sol (out real system), and reaching the highest level you can badge wise. But even after doing all these, you could continue to play on. I assume you could (if you could reach them there seem to be a lot of planets not in reach mostly near the core) conquer all the planets in all the galaxy, that would take some time lol, but i assume the game would still go on with eco disasters, pirates and so on.
Short answer No it never ends unless you stop playing. or start a new species which i do all the time since you can reach space on hard in like 3 hours, i dont really get to into or attached to any certain creature.
