Of course. At the top of that list under
Tools > Preferences are two blank spaces for you to add the "Replace" and "With" values.
Of course, you'll need to be able to paste a single character for the "neater looking" fraction. You can use the character map that comes with most OSes, or there are a few sites out there that can display lots of different characters for you. (Unfortunately, it seems that in most cases there are only fractions available for halves, thirds, quarters, fifths, sixths, and eighths, which Google already has in the list.)