No, because Patrick is lazy most of the time. Look at the episode where him and Spongebob took care a clam. While Gary eat a lot.

but squidward himself can represent each of them:

Greed – well, i can only think of that time that he wanted the cardboard box and the paper because Spongebob made it look really good
Pride – That one time that he lived among other squids or every time he does his artistic thing
Lust – Handsome Squidward
Wrath – Always
Sloth – He sleeps at his job and neglects most of his duties not related to his interest
Envy – Squidwilliams, no need to say more
Gluttony – That Krabby Patty burger episode