Yes, private schools have an advantage, clearly.
Huskerfan pointed out a disadvantage, but my opinion is that the advantages outweigh the disadvantages. That is why some states, like Oklahoma, do not allow private schools to compete in the state qualifiers. They can compete with anyone throughout the year but not at state. They clearly have unfair recruiting advantages. Oklahoma knows this and they are saying "if you want the "unfair" advantages that come with private schools, you must consider this....".