Yes, Headphone (1) Pro supports fast charging.
With a 5-minute charge:
With ANC mode off, the headphones can be used for 4 hours continuously.
With ANC mode on, the headphones can be used for 2 hours continuously.
Test Conditions : Measured under AAC mode at 50% volume. Charging and battery tests are based on internal results from Nothing’s labs (25°C or 77°F). Actual battery life may vary depending on volume, frequency, output source, environmental interference, product features used, and usage habits. Actual experience will depend on individual use.