Yes. Since the 1099-Q was used for qualified expenses, it is not necessary to enter the form at all. Yes, having $4k or more left for you to pay is ideal for maximizing the AOTC. The 1099-Q also goes towards room and board which leaves more room. Usually room and board will be more than that.
See page 52 for qualified distributions at IRS Publication 970, Tax Benefits for Education & Guide to IRS Form 1099-Q: Payments from Qualified Education Programs.
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