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No. Georgia Tech does not consider need or the lack of need in its admissions decisions. Outside of the Tech Promise program, Tech also does not commit to meeting the need of admitted students.
@IZD123 Many full pay out of state students with all As and ACT of 36 are rejected if they want a popular major and apply regular decision. Checking the box that you can start Tech the summer after your 12th grade year may help you get admitted but paying cash does not help at all.
Since GT does not offer much in the way of financial aid I doubt it matters. Being full pay would mean you are not instate which lessens your chances.