Does PG have a database

I have working PostgreSQL databases on 3 of my ~30 Linux boxes. I want
my software to be able to determine which of my 30 boxes have functional
databases on them. Since Pg is part of the baseline distro, merely
checking for the existence of an executable doesn't solve my problem.

I tried looping through my list of hosts and running the command:
psql -h $host --list
but this fails on a box with a database with the same error code as on a
box that doesn't have a database, if my PGUSER isn't set and my login ID
is not the username of the database. The PGUSER setting might differ
for each host, so specifying this in the software is not practical.

Bottom line: What trick can I use to determine whether a box has a
living, breathing Pg database if I don't know the DB owner?

Mark