Under the Asbestos Hazard Emergency Response Act (AHERA), is the installation of carpet over damaged A/V floor tile an enclosure?

No. An enclosure is defined in 40 CFR part 763.83 of the asbestos in schools rule as “an airtight, impermeable, permanent barrier around asbestos-containing building material (ACBM) to present the release of asbestos fibers into the air.” Carpeting is not impermeable, permanent, or airtight.