No. Purchasing "green power" does not make your household carbon neutral.
Imagine a two person household in Indianapolis. Without more qualifying information, their total carbon footprint is about 50 mtCO2e annually. Only 5% of that is from electricity (source).
Purchasing the green option from the utility may be a good idea (although the devil is in the details as far as how quality those RECs are). Even if they did, however, their carbon footprint would still be around 47 mtCO2e annually: