no. it's every hand you're dealt is counted.
I'm sitting on 29x $2 tickets and I haven't played a ton of hands on GG lately.
I'm guessing fastest way to get the $2 ticket is to play Rush & Cash tables. If a person knows a bit about playing on 100bb stacks they should be able to make a few $'s from playing even just the $0.01/0.02 tables while getting their 300 hands for the day.