Seven, probably not, but that's how old my oldest son was when he began reading the series. From the first book there have been scenes of fairly graphic violence. That's why I read all of the books before my son did--I wanted to know what he was going to be exposed to so we could discuss it together after.
My son is now nine and he finished Deathly Hallows last night (I finished it Saturday). He finds the dementors most frightening and was saddened by all the deaths, but he loved the book.
The earlier books I could see being okay for seven year olds... The later books (no way).