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AP would prevent the damage dealt from Damage Shield from being reduced, yes.
However, the damage is not unavoidable. "Unavoidable" is a specific game term and AP does not have anything to do with that term.
Nitpicky, maybe, but pretend for a second that there is some BFC that reduces unvaoidable damage, increases it, or otherwise keys off of that term. AP will not be affected by this theoretical BFC.