The duration that your battery will last depends on two things: the battery's usable capacity, and the amount of power you're using.
The amount of power is fairly easy to figure and you can do that before you go away. Generally work on the worst case - so if your fridge will draw 3 to 4 amps 50% of the time, then count on it drawing 4 amps 50% of the time.
The usable capacity is the trick. Different battery types affect this greatly.
On the low end of the scale is a flooded deep cycle charged by your car. The car will only charge the battery to about 75% of its capacity. These batteries can only be discharged to about 50% of their capacity, because beyond this charge level they start to sulphate badly. This gives you just 25% of the rated capacity, or 50% if you charge it with a mains or solar charger.
On the high end of the scale is the spiral-wound AGM batteries charged by a mains charger. An AGM can be discharged to about 20% of its remaining capacity - so a fully charged AGM can deliver 80% of its rated capacity. If you charge this with your car - so by the time you get there, it's charged to 75% of its capacity - it's still got 55% of its rated capacity available - more than a mains-charged flooded battery.
The obvious difference is cost. We bought a 160Ah spiral wound Optima AGM battery - $549 at Autobahn, and $499 at Rays Outdoors. Flooded cell batteries would be a half or less of that cost.
Do NOT use gel batteries. Any slight overcharging of the gel battery causes bubbles to form in the gel - and since the gel is a gel and not a liquid, the bubbles are permanent and irreversible. Your alternator cannot charge a gel reliably.
Apart from that - go for it. Portable power packs are handy because you can relocated them, to keep the cabling tidier, and shorter (the shorter the cables the better), and out of the weather too!
