Members/Users do not have to be actually logged in to make database connections. Just viewing your site main page will look to the database for requested information. Do you have blogs, news, articles, polls, site stats, etc on your homepage and other pages? If so then this info is stored in the database. When someone visits your site whether member or guest(not logged) they are pulling info from the database which is displayed in their browser.

So it could potentially be random visitors looking see more at your site. It could be crawlers and bots, it could be anything really.

If you look at the last part about /index.php requested paramaters, it almost sounds like it's someone voting on a poll or something to do with the polls that made the connection. And unless you have made the polls block only visible to members anyone can actually vote, and over and over again if they want. Just for the heck of it really.

Most hosts do limit the number of mysql connections in a shared hosting environment. This will vary from host to host, but basically it helps keep 1 website from using all the mysql resources, and keeps say for example 20-30 connections available per account.

Anyway just some thoughts and ideas.