Quoted: But I was wondering if I could just hook it up to a deep cycle battery and get more runtime.
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You can indeed, and the difference in runtime is...well, impressive.
The average UPS gell-cells are rated for 7 to 15 amp-hours, whereas the average Group 27 deep-cycle battery is rated for around 110 amp-hours. This translates into roughly 7 to 16 times longer run-time, for any given load.
However, there are several disadvantages:
1. Most deep-cycle batteries aren't sealed, which means that you'll have to add water every few months.
2. Non-sealed batteries give off explosive hydrogen gas, which makes good ventilation essential whenever they are located indoors.
3. Non-sealed batteries are messy - the connections tend to corrode, and spilled electrolyte can ruin your floors, your clothing or your skin.