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First, note that your solution doesn't really work. Consider this test file:

$ cat test1
Network
Administrator Network
Administrator

And then run the command:

$ sed '
 s/Network Administrator/System User/
 N
 s/Network\nAdministrator/System\nUser/
 s/Network Administrator/System User/
 ' test1
System
User Network
Administrator

The problem is that the code does not substitute in for the last Network\nAdministrator.

This solution does work:

$ sed ':a; /Network$/{N;ba}; s/Network\nAdministrator/System\nUser/g; s/Network Administrator/System User/g' test1
System
User System
User

We can also apply this to your guide.txt:

$ sed ':a; /Network$/{N;ba}; s/Network\nAdministrator/System\nUser/g; s/Network Administrator/System User/g' guide.txt 
This guide is meant to walk you through a day as a System
User. By the end, hopefully you will be better
equipped to perform your duties as a System User
and maybe even enjoy being a System User that much more.
System User
System User
I'm a System User

The key is to keep reading in lines until you find one that does not end with Network. When that is accomplished, the substitutions can be done.

Compatibility Note: All the above use \n in the replacement text. This requires GNU sed. It will not work on BSD/OSX sed. [Hat tip: Philippos.]

Multiline version

If it helps clarify, here is the same command split over multiple lines:

$ sed ':a
    /Network$/{
       N
       ba
    }
    s/Network\nAdministrator/System\nUser/g
    s/Network Administrator/System User/g
    ' filename

How it works

1. :a

   This creates a label a.

2. /Network$/{N;ba}

   If this line ends with Network, then read and append the next line (N) and branch back to label a (ba).

3. s/Network\nAdministrator/System\nUser/g

   Make the substitution with the intermediate newline.

4. s/Network Administrator/System User/g

   Make the substitution with the intermediate blank.

Simpler solution (GNU only)

With GNU sed (not BSD/OSX), we only need one substitute command:

$ sed -zE 's/Network([[:space:]]+)Administrator/System\1User/g' test1
System
User System
User

And on the guide.txt file:

$ sed -zE 's/Network([[:space:]]+)Administrator/System\1User/g' guide.txt 
This guide is meant to walk you through a day as a System
User. By the end, hopefully you will be better
equipped to perform your duties as a System User
and maybe even enjoy being a System User that much more.
System User
System User
I'm a System User

In this case, -z tells sed to read in up to the first NUL character. Since text files never have a null character, this has the effect of reading the whole file in at once. We can then make the substitution without worrying about missing a line.

This method is not good if the file is huge (usually meaning gigabytes). If it is that large, then reading it all in at once might strain the system RAM.

Solution that works on both GNU and BSD sed

As suggested by Phillipos, the following is a portable solution:

sed 'H;1h;$!d;x;s/Network\([[:space:]]\)Administrator/System\1Us‌​er/g'