To a freewheel, there is no difference between coasting and backpedalling. If it is so gummed up you can't backpedal, it shouldn't freewheel either - or at least not easily. If you coast with your feet off the pedals, does the crank spin on it's own?

Take the rear wheel out and spin the freewheel by hand, then try to pull the chain away from the jockey wheels and spin those, that should tell you if anything is sticking.