Addai could definitely be an every down back. The reason he didn't get a lot of carries at LSU was because they switched up RBs a lot. But he had games where he had a lot of carries. Also, he plays well vs. good defenses.
32 carries, 156 yards vs. Florida (10th ranked rush D) Also 3 catches for 37 yards.
24 carries, 130 yards vs. Miami in the Chick-fil-a Peach Bowl (15th ranked rush D I think)
16 carries, 84 yards vs. Tennessee (2nd ranked rush D)
He also had a pretty good game vs. Auburn, who was ranked 16th in rush defense.
A good running back in the SEC is a great RB anywhere else. The top SEC RB in yards was 17th overall in the country