The answer is "No", in fact it's a very bad idea!
Burning treated lumber, petroleum products, painted wood, trash, and such, releases toxic chemicals into the atmosphere (including your home!), and could cause other damage, as well.
For example, a catalytic combustor in a wood stove can be destroyed by certain chemical agents found in these items.
Fireplaces and stoves aren't designed as incinerators, and it is neither safe nor environmentally sound to use them as such.
Stick with seasoned dried firewood for your heating needs. This way you will be protecting your health, and your neighbor’s health as well.