Sure, technically - but if a file's sensibly broken up into lines on semantic boundaries, "git diff" will at least let you think of it like it only rewrites the bits that actually changed. If you're versioning a file with no linebreaks, the diffs would be meaningless ("minus everything, plus everything"), which is an unfortunate loss of functionality.
I guess you could just smudge/clean it through a JSON linter. You probably don't even need smudge, since Chrome likely has no problems parsing indented JSON.