I'm not sure there's a definitive answer to that, but my guess would be no. Problematic Word files seem to work better the earlier the version of ID you place them in, which implies there's something odd about the Word file, and it won't get better.
Three days agi I edited a Microsoft Word 2007 file that contained text and pictures on my work's notebook computer, running Windows 7 Professional, Microsoft Office Professional 2007 and Adobe InDesign CS4.
I then opened the same file on another computer running Windows 7 Professional but loaded with Microsoft Office Professional 2013.
I saved the file as a .docx, but allowed Word 2013 to save it in the newest format. I also saved a copy as "Word 2003 and earlier (.doc)".
On my work laptop, I created a file in Adobe InDesign CS4, and chose the Place command, and placed each of the three Microsoft Word versions in different text frames.
The Word 2013 file produced a totally blank text frame. InDesign imported no text or pictures. Just a number sign
The file, opened in Word 2013, but downsaved as Word 2003 (.doc instead of .docx), placed the text correctly but did not import the picture.
Then, on my own laptop, equipped with the identical version of Windows 7 Professional, pened a copy of the InDesign file in Adobe InDesign CS6 (8).
Deleted all imported text and created three blank text boxes.
Again, chose the Place command from the file menu
InDesign CS6 seamlessly imported all text and pictures from the .docx file saved in Word 2013.
It did the same for the file saved as Word 2003 and the file saved on my EPA computer as a .docx in Word 2007.
So newer software does make a difference.