How to conditionally show a views field?
You could do this by creating a views row template for your view and then adding in logic to test whether or not a thumbnail exists. This also lets you style the row output differently so you don't have a gap where the image would have been. 

Here's the handbook section on views theming:

http://drupal.org/node/352970

but your logic in the views template would be something like:

  if ($fields['field_&lt;video thumbnail field name here&gt;']-&gt;content) {
      &lt;output image&gt;
  }