when it comes to pathogens, fresh air is the best defense because it disperses the little guys to a near-harmless level. so if you're ever riding with someone who hasn't been vaccinated, simply roll the windows down. when it comes to smoking or pet dander, I seriously doubt that that tiny fan is going to move enough air to remove the smells that are in your seats and carpet.
I would pass on it. but if it makes you feel better and more proactive, then I guess go for it.