It could last 4 years if maintained properly or it could be dead in a few weeks. The key to long life for any wet cell battery is keep the water above the plates, do not discharge it below 12v or leave it that state very long. If you can do this, it should last a year easy. If however you allow it run down too far or too often, it will slowly die with each occurence. That's what is great about deep cycles, they tolerate this 100 x better than starting batteries.
I would plan on $10+ @ day for gasoline to maintain your current setup properly, more in the winter. RV generators are terribly inefficient, especially when used just to charge a battery.