Yes, absolutely. You nailed the real constraint on the head already, it's all about power consumption. Some things to consider:
Don't forget to factor in power consumed by the inverter itself, in addition to the item you've got plugged into it. If you've got a good amp probe you can measure this directly, but keep in mind you'll need a good "True RMS" meter to get an accurate reading of DC current.
Consider using a deep cycle battery rather than just a standard car battery. They're more expensive, but will work much better for your project. The battery label should indicate "amp hours". You can use this to calculate how large a battery you'll need to carry your load over night without discharging the battery.
Many inverters have a built in low-voltage shutdown feature that will turn the inverter off well before the battery is fully discharged, so account for that with your battery size.
Finally, a question, you mentioned that your camera had a DC line in. If that's the case, why mess with the inverter? If I understand correctly you're going solar panel (12VDC) -> car battery (12VDC) -> inverter (12VDC to 120 VAC) -> plug in transformer block (120VAC to some voltage VDC) -> camera, right? IF that's the case, you could go solar -> car battery -> resistor -> camera. It'd be more energy efficient. For that matter, if your camera isn't pulling all that much power, and I assume has a rechargeable battery already, you could probably do it with a solar panel and a resistor.
Email me directly if you'd like, I've been down this road before.
I got a similar setup on my truck, powering fans that cool my inverter and battery bank, when I don't drive the truck.