Yes, coach is a Scrabble word!

Verb

1. Teach and supervise (someone); act as a trainer or coach (to), as in sports

2. Drive a coach

Noun

1. (sports) someone in charge of training an athlete or a team

2. A person who gives private instruction (as in singing, acting, etc.)

3. A railcar where passengers ride

4. A carriage pulled by four horses with one driver

5. A vehicle carrying many passengers; used for public transport