Not exactly, but you can do this:
- In the Administration block, under the Reports menu, select Course Participation.
- Select the activity you are interested in.
- Next to Show only select "Student."
- Next to Show Actions, select "Post."
- At the bottom of the list, click "Select all 'No'"
- Then, with selected users, "Send a message."
This isn't exactly the same as completion criteria, but it will let you send a message to all students who can't have completed the activity because they haven't submitted anything to it. (If viewing the activity is sufficient, e.g. it's a required link, then next to "Show Actions" select "View."
I hope this helps!