Can my settlers (especially the supply line units) die?

Your settlers at home can die. Note that once a 'settler' has been assigned to a supply route, they will be a 'provisioner' the next time they are loaded.

Provisioners who are away from a settlement can't die. The can get knocked down for a few seconds like other essential NPCs, but they get right back up. Currently, the closest I've observed this is at the Rotten Landfill (east and slightly north of the drive in).

It may be that:

a) Provisioners are just essential always

b) Provisioners who are outside a certain range of a settlement are essential, but can be killed when close to it.

or c) Provisioners who are outside a certain range of their home settlement and/or destination are essential, but can be killed when close to them.

Clearly, more testing is required, but given what I know about how the essential flag works, it's a pretty safe bet that provisioners are just essential all the time, and therefore can't be killed.

No, settlers can't be killed by raiders or by anyone apart from you. Apart from the case if you failed to defending quest. They only knee like companions. But you can kill them, and it can happen accidentally during fighting so don't ever use grenades if your settlers are near, they have very low health and also better always to use vats in settlements.