I use paper tickets and in seven flights since 9/11 I have yet to check-in up front. On the stub portion of a UA ticket it does say "Boarding Pass," which seems to be sufficient for security.

In the event security lines are very long, it could be wise to check-in at the front though so they know you did check-in on time and are coming. Some people have reported planes being held because so many people who had checked-in for the flight were held up by security. If you haven't checked-in, but are in the security line, they have no idea that you're there.