Ryan Anderson does have faults. He is not a good defender. He is an average rebounder for a stretch four. However, pairing him with Anthony Davis gives the Hornets two frontcourt pieces that fit well together.
The beauty of having a defensive anchor is that it allows a team to ignore defensive faults in their other players.
Having Tim Duncan allowed the Spurs to tolerate Tony Parker's matador defense and win three titles. Bill Russell was a savior for the first group of title-winning Celtics. With nonentities on defense like Bob Cousy, Frank Ramsey and Lou Tsioropoulos, Russell had to make up for a lot of defensive deficiencies.
That ability to cover up others' poor defense is what many (including the Hornets) believe Anthony Davis has.
Therefore, Ryan Anderson's defensive liabilities and his below average (ordinary for stretch fours) rebounding production should not pose much of a problem for the Hornets.
Looking at the NBA landscapes, the NBA lacks traditional post-up big men who consistently create high percentage looks. Also, few teams have two high quality post-up big men. The Lakers and Grizzlies are currently the only ones. The Hornets will not have to worry about Anderson getting manhandled in the post.
Ryan Anderson brings three-point shooting and floor spacing to the Hornets. His three-point shooting will bring opponent big men out to the three-point line and away from the basket. This not only removes those defenders as rim protectors, but also puts those big men in an uncomfortable situation having to guard on the perimeter.
With Anthony Davis' perimeter skills (remember he was a 6'2'' guard in high school before the growth spurt), the Hornets have the ability to empty the entire paint and open up driving lanes for Eric Gordon (assuming they match the Suns' offer sheet) and Austin Rivers. Big men will have to travel a much farther distance to cut off a drive to the basket. Therefore, once the Hornet guards get past the initial defender, they'll have a clear path to the basket against most teams in the NBA. If the big men attempt to cut off the drive, they will give up perimeter shots for Anderson and Davis (who has excellent form on his jump shot).
Only highly complex defenses (Boston and Chicago) or super athletic defenses (Miami and Oklahoma City) will be able to both prevent penetration and effectively help if the initial defender gets beat. As Davis develops more of a big man's offensive game, the Hornets will become a more flexible offense and this will increase the difficulty of defending the Hornets.
The New Orleans Hornets are far from a complete team. They need to add perimeter defenders (particularly at the small forward) and they must find quality role players to come off the bench.
However, with a potential superstar in Davis, a star in Eric Gordon, a wild card in Austin Rivers and a fantastic complement to their superstar in Ryan Anderson, the Hornets look set to begin their rise up the Western Conference.