Once your written expires if you haven't obtained your ATP yet. As long as you complete the written prior to 1 Aug 2014, you then have 24 months to complete the practical without having to go through the entire new training process. To clarify, the new sim training IS NOT the ATP ride itself, rather it is just additional training required to be completed before taking the written after 1 Aug 2014. You would still need to complete the practical, but my guess is these training programs will offer the ATP ride in the sim at the end of the required training. Straight from the source:

Ref FAR 65.155(d) "An applicant who successfully completes the knowledge test for an airline transport pilot certificate prior to August 1, 2014, must successfully complete the practical test within 24 months from the month in which the knowledge test was successfully completed. An applicant who passes the knowledge test prior to August 1, 2014, but fails to successfully complete the practical test within 24 months must complete the airline transport pilot certification training program specified in §61.156 and retake the knowledge test prior to applying for the practical test."