At the end of the mission on Mars, a Cerberus agent is running away with the data about the Prothean device. I was unable to catch her. Is it possible to catch up with her before she reaches her shuttle and does it matter if I do?
No, you can't catch her. As a Vanguard, I used Charge to stay within 0-5 meters of her through the entire chase with no effect. She will always reach her shuttle and trigger the cutscene that follows.
No it is impossible to "catch" her during the chase as what what follows is part of the storyline.