When does PostgreSQL write logs?
No, if PostgreSQL writes logs, then it writes basically real-time.  For example, if you open a log file with less and press ShiftF, you will get the newly written rows flowing in.

That you don't see anything in the logs can be caused by a few things, but first be sure you have read through the relevant documentation and set up everything accordingly.  There and in postgresql.conf you can also check where the DB writes the logs and so on.  Be aware that some configuration options need server restart or DB reload to take effect.