Yes I think you have enough time to visit the terracotta warriors. Two choices:
1.Take the tourist bus at the railway station square to the terracotta museum,which may take about 1.5 hour,allow 2-3 hours visit there, then get on the return bus before 3:00pm,arrive the railway station at about 4:30,take a taxi to Melody Hotel(right beside the Bell tower), take the shuttle bus which depart at 5:00,then hopefully you'll be at airport before 6:30.However, this seems a little tough for you if it's your first time to be in Xi'an, you may waste a lot more time to find out the direction,or to wait for the bus.
2. Book a one day tour beforehand.You'll then have more time to visit the site and no worry about missing the flight.

And for one day tour, this travel china guide should have such service? I just noticed they have recommended Xian packages right on this page.