Increasing the fan speed on a passively cooled card (so no fans, relies on convection for cooling) will have no effect.
Unless you are referring to a reference design card, which look like this.
http://www.newegg.com/Product/Product.aspx?Item=N82E16814130809
Increasing the fan speed will increase cooling. That circular "hole" at the end is actually a blower fan. Their different to normal fans in that they create a higher air pressure, but are louder and dont cool as well, but have the benefit of ejecting hot air outside the case.
Increasing the fan speed wont have any negative side effects other than it will be louder.