It would affect receiving files, yes, since system-backup does not allow writes. Access to arbitrary dot files in $HOME is not a supported use case for snaps (see Process for reviewing classic confinement snaps).
As mentioned in this topic, this would be a documentation point for your snap: either use the pipe method or have the user put the file in another location that is allowed to the snap. croc could be updated to guide the user if it detects it is running as a snap and tries to access a top-level dot file/directory in $HOME.