Just for the record, you can only have a pick-up bar at the beginning of a
movement, the idea of a pick-up bar in the middle of a piece makes no sense.

"I'm writing a score in four sections. Each section begins with a quarter
note at the end of a bar. Is there way to have that quarter note at the
beginning of a system (similar to a pick-up bar) and have the system before
ending with a three quarter note bar. In other words, I want each section to
be on a system all by itself."

The answer is yes. Hymnals are often laid out like this when the phrases of
the hymn always start on up-beats (e.g., Bach Chorales).

All you need to do is select the note which you want to be at the beginning
of the next system and then choose Plug-ins > Other > Split Bar.

Make sure that the following check boxes are checked:
Add system break at split
Use same bar number for split bars.

Press the OK button.

What happens is that the bar containing the note you selected is split into
two new bars. The first bar will be three quarter notes long and the second
bar will only be one quarter note long. A consequence of this is that the
note in the quarter note bar will have a rhythmic position of quarter 1.

A bar number change is added to the one quarter note bar so that it has the
same bar number as the three quarter note bar. This is done to ensure that
the two shorter bars are treated as one. This means that the same bar number
will appear twice as you arrow through the score.

A system break is added at the end of the three quarter note bar. This makes
sure that the one quarter note bar is at the start of the next system.

Hope this is clear,