It is possible to create a new comment in pdf or access existing comments and read their properties directly from VBA. But Adobe does not let you change properties (position, content, type, etc.) of existing comments.
A workaround is to make a folder level javascript file, put a function in it and call that function from a VBA macro. I attached two files as an example. You need to put ShiftComment.js file to the javascripts folder in C:\Program Files (x86)\Adobe\Acrobat 11.0\Acrobat\Javascripts and restart the Acrobat. Since you are using Acrobat DC, path to this folder may be different.
When you run VBA macro in visio file, it opens a file explorer for you to select a pdf file. Then it will ask the shift value. Then it will pass this value to the function in javascript file. Javascript function will read all the comments in the pdf and shift them to left or right based on the value you entered. Positive values will shift the comments to right and negative values to left. Note that for a 8.5 x 11 PDF page:
x-axis range is 0 - 612 pts
y-axis range is 0 - 792 pts
(1 inch = 72 pts)
Feel free to ask if you face any problems.
Tested on Visio 2013 Pro, Acrobat XI Standard on a Windows 7 64 Bit machine.