Personally I would have 'thought' not, as they don't have any memory storage and processor as such to execute code. That would have to be done from the other system and executed on your system.
Public charging stations are ideal if your phone is low on battery. Unfortunately, research has shown that they also have the potential to be useful tools for hackers.
This is because USB charging stations can also be designed to both inject malware and steal data from anyone that uses them.
So potential not actual and I believe the other remarks also apply to cables, etc...
Juice jacking is possible because of how USB ports are designed. On a phone, they are primarily used for charging but they are equally suitable for transferring data. This means that whenever you plug your phone in to charge, you are also potentially opening the door to data transfers.
It's considered a potential threat, not an actual threat, because most phones now ask permission before data transfers are initiated.
You have to consider that the threat isn't from the cables/charger as such but the source (computer) executing code (providing the juice) to make any transfer and execute commands to be run on the target system. Don't lose site of the fact that the target system could/should have its own protection Avast (presumably) in your case.