Do AWS backups of large empty volumes take longer than small ones?
Firstly I would argue that backup time does not matter,  as it usually doesn't correlate with the restore time. 

In regards to restore time,  snapshots restore on volumes almost instantly,  as data is only copied onto the volume from S3 when requested. 

So as long as you only request actually used data from the volume, it would only matter how much data is used on the volume to determine the time to restore. 

This link explains the process well https://docs.aws.amazon.com/AWSEC2/latest/UserGuide/ebs-restoring-volume.html