POLLEN IS EVIL. THAT'S WHY IT WON'T BLOW AWAY.
Actually, as you surmise, some pollen is "sticky" and once it lands on a surface it tends to remain.
In our area one of the really troublesome pollens, from an allergy standpoint, is oak pollen. As you will see from the microscopic photo below, oak pollen has "stickers" which make it stick where it lands. One of the really troublesome effects of this is that it sticks in the sinuses of allergic people. That is why it can be very helpful for people who have this allergy to rinse out their sinuses with a Neti Pot, available in local drug stores.