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Its ok to throw it on.You don't even need the rear one,for the most part lowering your car will take care of all that extra handling you need.Make sure you use good polyurethane bushings like the ones from energy suspension when you install.Other wise it wont really make any difference.
Tower strut bars are designed to eliminate “flex†in the vehicle chassis. A tower strut bar allows the vehicles suspension and chassis to remain rigid even through high velocity turns. On the Neon, the rear tower strut bar will be more affective than a front bar, however, both are recommended along with upgraded sway bars. But to answer your question, no, you dont need both of them...