What do you mean by "...second and fourth planting be a little in front..." I don't understand that question at all. Maybe you could show with a simple sketch what you are talking about.

Sorry. I can plant 5 arbors in a straight row. Or, I can move 2 up a little from the others. Kind of like a zig zag. Did that help?

Makes sense to me, but I have a tendency to visualize everything before I do it, so no picture needed.

In answer to your question~I think it would be more esthetically pleasing if they were in a straight line. I seem to prefer only smaller plants usually in a flower bed done in a zig zag pattern.

With the understanding that aesthetics are entirely in the eye of the beholder, I'm going to disagree :-) A staggered or uneven planting is going to be much more visually appealing. A row of plants always looks artificial - nothing grows ina straight row in nature - and with something large and evergreen like arborvitaes that translates to a green wall.

A privacy screen tends to be a less defined and more informal approach than a sculpted hedge or fence for privacy purposes. If you have the space, stagger the plants.

I seem to faintly recall something from my distant formal design education past that planting in rows was a distinct no-no.........unless you were creating a formal hedge :-)

I'm going to disagree with gardengal a bit. I don't think that emulating nature is always the goal in landscaping. Often it's creating something "architectural" out of plants. The plantings should fit the space and since I can't see it, I can't offer a preference. It's on you, Candle, to determine the best fit. It might be a single row or it might be the staggered double row. If you don't have room enough, the double row will not be the better choice.