No, she dated Logan because he was pretentious, self-righteous asshole who can't stop complaining about his rich dad, but has no qualms with living the good life off of said dad's money. While Rory had ambitions to go to Chilton, Yale, ambitions that perhaps Dean didn't really get in the end, the old!Rory chose those elite school because the education they offered. New!Rory hijacked a yacht and dropped out of Yale because Logan's dad said some mean things. The dynamic of the Rory-Logan relationship centered on somewhat-witty-but-dry-banter, acting like a boring married couple that loved the life of luxury. Old!Rory would have laughed in New!Rory's face at her patheticness.