Not quite. Early had a chance to occupy Culp's Hill, which was on the extreme right of the Union line, on June 30th but never did. In several attacks over the next two days he failed to take Culp's Hill, and one of the soldiers who died trying to capture it was a soldier in the 2nd Virginia named Wesley Culp, who's family owned the property.
The battle for the Round Tops gets a great deal of attention in the books, but that for Culp’s Hill was every bit as crucial, as the loss of either would have flanked the Union Army.