Is it true that flushing tampons down a toilet will stop it up and cause an overflow?

Yep. Same for sanitory towels. It happens and it's not fun.

EDIT

"75% of blocked drains are caused by flushing sanitary protection,"
Disposable menstrual products - The issue (http://www.menses.co.uk/issue.htm)

This site also mentions other problems associatedwith this practice.

Yes!!