wordpress with no visitors and server resources

Pretty sure that no visitors = no consumed resources.

Thanks for the quick reply! I was just wondering if it does anything scheduled. Would something like wp-cron.php run by itself on the server?

Yes, cron would run, and obviously your visits would be tracked. They use minimal resources, though. Not enough to cause any problems, otherwise no one would ever use localhost installs via MAMP or XAMMP.

I thought wp-cron was triggered by visits?

Whoops! Right! wp-cron does need visits!