I've ridden the Tour de Tahoe version which is the same route.
Based on the info from http://www.bikethewest.com/AMBRR.html the climbing totals 4,400. It's not a difficult ride. If you take your time and drink lots you won't even notice the elevation. If you are training with hills, you'll do just fine.
The 72-mile America’s Most Beautiful Bike Ride circumnavigates the highways clockwise around Lake Tahoe in both Nevada and California. It includes a challenging 800 foot climb to a rest stop overlooking Emerald Bay and a 1,000 foot climb to Spooner Junction. There are also many short rolling ascents and descents totaling over 2,600 vertical feet of elevation gain! The altitude ranges between 6,300 feet and 7,100 feet above sea level and the ride is recommended for conditioned recreational bicyclist, not for beginners.