How close to zero? 1 MWh at 100% efficiency is enough to convert 180 kg of CO2 to ethylene (note this only produces 51 kg ethylene). Annual excess carbon emissions are 36.8 trillion kg of CO2. At a cost of $0.10 per MWh, which is about 3-4 orders of magnitude lower than it currently is, that's still $20 Billion per year. A cheaper pathway is still going to save an incredible amount of money even if solar power got ridiculously cheap.
The energy costs are only part of the equation, though. Especially if your plan is to use excess renewable energy, the cost of your plant is a much bigger concern, because you can't run it all the time.