Importing LARGE quantity of data into a PostgreSQL database
Log files in /var/log/postgres are only for your information (in a standard installation) and do not serve the system itself, especially not "ACID compliancy". They need to be writable once configured, that's all the server needs.

There are a number of settings in your postgresql.conf that govern what is logged. Most of them can also be set at the command line to overrule the setting in the config file. We are not talking about WAL files, which are not usually placed in /var/log/postgres.

I would drastically reduce the verbosity in your case. Among others, I would set (and reload the server):
log_statement = none

Depending how you import the data, you probably need to do more than that. Look at:
log_min_messages

To skip writing log files altogether you can set:
log_destination = 'stderr' ...

More in the manual.