Not really, there are some plugins you can get that can give elements random motion, but not specifically what you are looking for. If it is the exact same motion, separate the x,y,z motion from one of them and copy the keyframed z position and paste it onto all the other layers by hitting cntrl (cmd) + a and then paste
Then select the objects in the order you want to animate on and right click- keyframe assistant and then sequence the layers to overlap by 2-3 frames. If you are adding rotation, just follow the same steps for the z position
I hope that helps, I just got through animating about 600-800 elements, so I know how you feel. There is a gift of it on the homepage of http:\\cofchrist.org
Best,
Derek Boettcher
Creative Management
BTH Media Group
https://bthmedia.com