Yes, the plugin runs the WordPress Cron (it's built into WordPress) that runs when anybody hits the site when the cron time is fired. Here is what they say on wordpress:
"Schedules a hook which will be executed by the WordPress actions core on a specific interval, specified by you. The action will trigger when someone visits your WordPress site, if the scheduled time has passed."
So, when the cron fires, the plugin loads new posts for the Feed to Post feature.
If, instead, you are using the shortcode feature of displaying feeds on the site, this works a bit differently. Here, each time someone visits it pulls in the most recent feeds. You can set this to cache the feeds so that it will pull in the feeds then store them temporarily on the server (this is the option in the settings panel) and then new visitors will get the feed items from temporary memory.
I hope this makes sense and answers your questions.