Yes, busiest is a Scrabble word!

Adjective

1. Actively or fully engaged or occupied

2. Overcrowded or cluttered with detail

3. Intrusive in a meddling or offensive manner

4. Crowded with or characterized by much activity

5. (of facilities such as telephones or lavatories) unavailable for use by anyone else or indicating unavailability; (`engaged' is a British term for a busy telephone line)