Can I run a kitchen sink drain 19' through a hollow stud wall with seven 90-degree turns?
Drilling holes in 17 feet of studs to accommodate a 1 1/2 inch drain line would not be recommended. The sheer number of studs impacted, including two corners, would definitely weaken the wall, especially if it is a exterior load bearing wall. 

A second consideration with what is shown in your picture is that if it ever plugged it would be impossible to run a snake through such piping construction. 

It is common to organize the house layout so that the plumbing routing is optimized and clustered into one particular area. This way you avoid much of what you are proposing. You may want to seriously consider just where you plan to put this kitchen sink and drains.