Mt. Emei to Chengdu Airport (CTU)

Yes, the transportation is convenience.
You can take high-speed train from Emeishan Railway Station, get off at the airport directly. The train schedules are 07:20, 09:17, 10:48, 12:22, 14:10, 15:46, 17:31 and 20:47. It takes around an hour on the way. The ticket fare of first class seat is CNY68 and second class seat is CNY56.

You can buy the tickets when you arriving at the train station. But it's still suggested to buy the tickets online in advance in case the tickets may be sold out. But the official website doesn't have Chinese version. So you can ask help for TravelChinaGuide. They provide online ticket booking service. If interested, their contact information is bookingtravelchinaguide.com.