I like that you and others are thinking of alternative ways to power electrical systems. That said, here are my concerns with the plan:
1. Expense- Solar panels and a large deep cycle battery are not cheap, unless you have a connection somewhere to cheap materials. How much is the step up power supply.
2. Efficiency- Lead-acid batteries near full charge are less than 50% efficient at accepting a charge, and when fully charged, are about 50% efficient at discharging. A near-full-charge\discharge cycle can be as low as 25% efficient at converting your input energy into useful electrical energy. Efficiency raises significantly as the battery is discharged more deeply, but this is not good for even a deep cycle battery. Like Old brought up, there is the efficiency of the step up power supply to consider too.
Solar panels are most efficient when angled directly towards the sun, and quickly drop in efficiency as they are angled away. Putting solar on the roof is not the ideal angle in the northern hemisphere, and there are plenty of objects that could shade the vehicle when parked.
3. Convinience- What if you want to go on a longer drive than normal? The solar would not provide enough energy to maintain the battery, so there is a limit to how far you could travel. At night, this would severely limit your range.
What I would like to do, and what I suggest to you, is to figure out how to wire in an alternator cutoff switch so that charging can be restored when needed. I would then buy an appropriately sized LiFePO4 battery pack to get you through your normal travels, and grid charge from home at night.
Here is a 12v 20Ah LiFePO4 for $110.
If solar interests you, the best thing to do is permanently mount PV on your property in an optimal location and angle, and then grid-intertie, or 12v charge.