Its more than possible, and it's very easy to do using vBulletin (the software this site runs on). You can make it so new users require email verification like you described, and you can easily customize the message it sends. You can even make the board send a "welcoming private message" once the user activates his account, and it only takes a few mouse clicks and keyboard strokes in the Admin CP. I find that coupling both of these really increases the chances that members will read what you're trying to get them to. You can make both the email and PM list appropriate rules/FAQ links with a blatant bold, red, large font "READ THIS STUFF BEFORE YOU DO ANYTHING ELSE" message at the top.
With some board modification and cleaver permission changes it's also possible to limit a users access until they've read certain topics and checked a "I verify that I've read this topic and understand it's meaning" box... You can also make it so the box isn't check-able until the user scrolls to the bottom of the page, or until a pre-set timer counts down.
vBulletin is very robust when it comes to user permissions and automation if you know how to use it correctly. So saying that it isn't possible with the current "setup" isn't accurate.