The PDF Connector allows you to modify the settings to read your PDF file as lines, segments and words.  The settings are very specific to how the PDF is constructed.  Once you have found the settings that allow you to properly grab the lines, segments and words from your document, you can read through them one line at a time.  Each segment or word has a Left property.  This will tell you the offset in the line for the segment or word.  With some detective work you can find the offset for your checkbox and then determine whether it is checked or not based on the value of the segment or word at that location.

It is very hard to tell you how to work with this without the actual PDF. 

I have been testing with your form.  By setting the word threshold lower (it is 2.2 by default) you can isolate the check boxes from the text next to them.  I don't know how they are represented when they are checked however. 

I set the Word threshold to 1 and this is how the words were delimited.  Notice how the checkboxes are highlighted by themselves.

Each word has a left value - the starting pica value.  If you read through the words, whenever the left value is less than the previous left value it means you are on a new line.  I use this to assign line numbers to each word.  Then you can index each word by line number and left position.  here is an example.

After doing all of this, it does not appear that the checkboxes present the check in text form.  I need to do a little more research for them.