Hi and welcome to FixYa, I am Kelly.
You will not damage the battery.. you will destroy your AC Adapter charging system because the Jump start system will draw more amperage than your AC Adapter can provide. The Jump start system will charge at a minimum of 2 amps up to a maximum of 6 amps. Your AC Adapter will only provide 1.3 amps max. I.e it will go up in smoke.
Thanks for choosing FixYa,
Kelly
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