Does caffeine consumption stress the liver in any way?

Not at normal doses: No more than any other compound that must be demethylated and oxidized. Some people are deficient in a liver enzyme cyp1a2 that renders them more susceptible to the effects of caffeine.

No: Multiple studies has proven that caffeine has a protective mechanism against fatty liver disease. I am yet to find any information linking caffeine consumption to liver disease. Because coffee is considered one of the most beverage consumed in the world, plenty of research were done on coffee which has other beneficial compounds.