Absolutely not; prices are set based on what the market can bear, completely independent of input materials. If a vendor makes a huge investment in widgets and no one wants to buy, it ends up being a sunk cost and they'll sell it below cost (because supply and demand).
Additionally, cost is defined as "the value of the next best alternative." Unless the network is at capacity, it costs me nothing when my neighbor uses e.g. T-Mobile's no-charge music streaming.
What's being proposed is called toll-free broadband and all parties have an opportunity go in.
Net neutrality, on the other hand, is a routing philosophy. It applies to routers. It says don't drop packets based on source or destination (dropping packets being how the Internet signals congestion and prioritizes in general). Toll-free broadband doesn't violate this rule.