They should grow, but as pointed out, not a great choice for a privacy hedge. They tend to grow wide, 6 or 8 feet, do you have room for them to be that wide? If not, they will need a lot of pruning every year to make a 'hedge.' All the pruning interferes with bloom, and the early yellow bloom is about the only special feature on forsythia.
I think you would be well to consider something else. Ask advice from a nursery, not the big box. or
Spring and fall both are probably fine for planting a hedge.