So, you will have an alternating design with nailers on both sides of the post?
I always liked that style. The fence looks the same from either side.
Are you talking about alternating from one side of a single side of nailers?
If you are planning on using only one set of nailers, you will have to consider the posts in relation to the pickets. You may have to rip some of the pickets to correlate with the posts.
Your description indicates nailers on both sides of the post. That will be the easiest and better looking design. Setting your boards at different spacing and using wider or more narrow boards will greatly affect the finished look of the fence. Draw up a few different picket width/spacing designs and you will see what I mean. Closer spacing or wider boards will give you more privacy. Spacing wider boards further apart will make it less private.
You can do this, the plan you have shown is good. At the joints though, you could butt the nailers together, ie. level, and splice them in an alternating pattern. Splicing the top nailer on one post and splicing the bottom nailer on the next post. That may look better because you will see the nailers in an alternating design.