Depends what you mean by overnight. Regardless of whether you use private transport or public or group tour, the shortest time period you can accomplish this in is two full days: Day 1 first part of morning go to Giant Panda Breeding Center for 2-3 hours, then down to Leshan in middle of day, arriving for Leshan mid-afternoon to rest of day. Overnight in Leshan town or at base of Emei Mountain. Day 2 Emei Shan for full day, returning to Chengdu evening of Day 2. Note that this will only allow you to tackle a selected part of Emei Shan so you'll have to decide in advance what you want to do there. Fuller coverage of Emei Shan would require you to stay a second overnight (basic accommodations on mountain) and then continue exploration part or most of Day 3 before returning to Chengdu.

Bullet train service between Chengdu, Leshan, Emei is undergoing testing right now and may be operational for visits late in 2014 and beyond. This would be a big improvement over the slow and infrequent standard train and the road options that are currently available. No firm service start date released yet, though. And it will still not change the overall time requirements of combining these three sites.