You can do
some process | logger &
to spawn processes and have their output directed to syslog. Notice that the default facility will be “user” and the default level “notice”. You can change them using the `-p` option.
The reason why this works without probelm is that the processes don't directly write to the destination file. They send their messages to the syslog daemon, which manages writing to the appropriate file(s). As far as I understand things, the atomicity would be line-based, i.e. every line of output from a process would go to syslog without interference, but multi-line messages might get lines from other processes mixed in.