Did you read my comment, they built the ark without even trying to find a way to stop the reapers it was never going to be a contingency plan they were going to flee as soon as the reapers arrive and not bother with saving the galaxy.
Who said anything about stopping it, its about having taking advantage of every possible opportunity to further his agenda which includes ensuring the survival of the organizations ideals and acquiring new tech etc.
Unless there is some official word on the ME4's scenerio, you're assuming that the ark was started during ME2. It is more likely that the ark project was either
a) something else altogether (eg. an experimental craft testing new FTL tech) and repurposed during the reaper war
b ) cobbled together after the reapers attacked (similar to how the rather massive crucible was built)
The reason being simply that the council's position was that reapers were fake. Much like how garrus' constant pleas were handled, a token force was probably assigned to projects like these until the reapers started their invasion
As for cerberus, whether they want to further their agenda is rather irrelevant. If the ark is supposed to be a last chance for species survival, as long as its not stopped, no one cares whether the STG, spectres, cerberus, etc get new tech from it. Think about it. The ark is the last chance for survival. That means the STG, spectres, cerberus as organizations are ALL expected to be dead during its launch. You would at best get a handful of agents from the various covert organizations simply because there is no room.
Add to the fact that during the reaper war, new tech was coming out of everyone's noses (scorpion, hovertanks, dlc armor, protean weapons, etc). Any new tech an ark project could supply would not matter much and by its purpose, new tech is not a major priority but rather how many people you cram in with a good chance to survive.
As for survival of cerberus' ideals, think about if you're huddled in a small room while shells and bombs are going off around you. Do you seriously care if the person next to you believes that dogs will rule the earth or that vegetables are sentient (or some other wierd idea)? If the scenerio is truly a council project to ensure species survival, everyone onboard that ship will work together because its simply in everyone's best interest.