Ideally pick-a-date pattern in mockup should have some UI improvements to make it easier to use by keyboard:
Escape key should act same as delete/backspace.
Time: possible to type time directly, with auto-scroll to appropriate slot, if applicable, since there are only two possible l10n scenarios: 24h and 12h (am/pm). Should be possible to type H:M pattern, (optionally followed by 'A' or 'P' in 12 hour locales).
Ideally pick-a-date pattern in mockup should have some UI improvements to make it easier to use by keyboard: