After 2 years, I am still wondering this, could anyone give me a clue how to do it?
Since buying plugins is not an option for my company, I can only find my way...
Yes, it can, but it's a bit complex... Basically it involves reading each word in the document and testing it for the various types of possible quotation marks.
A while ago I developed a tool that does that, and can even find when non-matching quotes are used.
Have a look here: http://try67.blogspot.com/2008/11/acrobat-quotation-marks-checker.html
In case you change your mind about spending a little bit of money on this (it's not a free tool), feel free to contact me directly.