I, too, wanted an easy way to find bad boxes. It is often necessary to correct them for publications.
The existing LaTeXTools package simply ignores the overfull/underfull warnings. You can see this in the source file:
392 # catch over/underfull
393 # skip everything for now
394 # Over/underfull messages end with  so look for that
395 if line[0:8] == "Overfull" or line[0:9] == "Underfull":
You have to modify that block of code so that it reports Over/Under-full messages, either as warnings, or by creating another list of messages specific for bad boxes. I ended up forking their project and doing the latter. You can download it here.
Update: Note that these changes were eventually incorporated into the official LaTeXTools package, so you can now enable them by changing the package settings as described by @Gauthier