Can a pretty bad deviated septum cause constant post nasal drip?

Possibly yes: If the deviated septum contributes to sinusitis, then constant nasal drip may occur. Your history of allergies may also contribute to this. If the drainage should become purulent or bloody, you may benefit from antibiotics.

Typically no: Septal deviations create airway obstruction if there is associated allergies, you may experience enlargement of your turbinates which may then give you post nasal drip if you do have seasonal allergies many people will elect to try over the counter products like Claritin assuming you have no allergy to it.

Post nasal drip: Post nasal drip is not caused by a deviated septum. Rather it is caused by allergic rhinitis. You can have your nose evaluated by a board certified otolaryngologist.