Can I ignore caching of a plugin in W3 Total Cache? [closed]

You can try fragment caching, from plugin’s FAQ:

Edit your templates to with the following syntax to ensure that dynamic features remain so:
Example 1:
<!-- mfunc any PHP code --><!-- /mfunc -->
Example 2:
<!-- mfunc -->any PHP code<!-- /mfunc -->
Example 3:
<!--MFUNC           -->
                                      echo rand();
<!--/mfunc -->
Example 4:
<!-- mclude path/to/file.php --><!-- /mclude -->
Example 5:
<!-- mclude -->path/to/file.php<!-- /mclude -->

But my personal opinion is just to get rid of overly dynamic stuff. Unless it’s key functionality (like in e-commerce) it’s usually useless eye candy.