Index deletion and Backup size
If you delete 40GB of indexes, then certain backups will be smaller, such as:


Full
File
Filegroup


Some backups won't generally be smaller, such as:


Log


Differential backups (Full, File, Filegroup) may or may not be much smaller as it depends if any objects those non-clustered indexes are created on are actually having data modifications happening.

Some backup sizes might not go down by 40GB, if for example compression is already being used or those indexes are on a read_only filegroup that isn't generally backed up via filegroup backups.

However, overall, the answer is "Yes, it should be smaller".