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Is the DI 5v, 1A? I think it will trickle charge from a standard USB port, which is 500mA. You may want to check; I know my Droid (1) is 5.1V, 850mA and it does weird things if it doesn't get 5.1V.
In any case I wouldn't chain it that way unless it's an emergency. Any charge/drain can shorten battery life, if only a little. A UPS is supposed to get replaced or a new battery every 2-3 years.
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