It all matters on how much wattage the inverter draws compared to how much the lights draw if it's cheeper to go through the inverter then your saving. how much is the question.
The inverter will always draw more power than the lights and the lights will pull as much power as they are rated for...
If you give the converter 100 watts it can only output less than 100watts, because it wastes some power converting it. It can never give you more power than you give it...
-Loki