Synchronous Commit, WAL archiving and statement_timeout

Hello,

I noticed something strange and I would like to understand what's happening.

I have the following environment:
- 2 PostgreSQL instance running in hot-standby with synchronous commit activated.
(further called Master & Slave)
- The archiving of the WAL files is activated on the master running every 5 minutes
- Slave is down

I set the statement_timeout inside my ~/.psqlrc:
$ cat ~/.psqlrc
set statement_timeout = 1;
commit;

When running an UPDATE statement (via psql) on the master, it hangs (psql seems to
wait a response from the slave) ignoring any value I set in my .psqlrc and the update is
done and written on the Master. Furthermore if I try (doing the same things in a small
script with a timeout on the call to PQexec) to make a call to PQcancel it does nothing
on the Master.

I expected the statement to timeout because the synchronous_commit wouldn't work
since the Slave is down while rollbacking on the Master.