It sounds like this person is miserable regardless of whether you report them or not. It appears they're entering a transition phase that involves eventual separation, so nothing you're going to do is really going to make things much worse - or any better. Does the MD know that this person has had a family loss? If not, you might mention that in an addendum.
'Really bad time' is vague - does this mean someone is going to get lectured? Do they care?
The last time I was working for a company as an employee I would bring up the Craigslist listings once a day at work. My interest in this was to see what skills were in most demand - I wasn't actively seeking anything. I was in and out of the site in three minutes most of the time. 'Significant' amounts of time would have to be more than 20 minutes a day outside of break times. This would be even more so if it was obvious they were submitting resumes and corresponding with hiring managers.
I've seen (but can't believe) that employers would continue to pay people that don't show up for work for weeks. You may discover that the employee is retained until they get a new offer, even if half their day is non-productive. The MD may not be in the mood to separate someone that has been there ten years+, even if the separation is justified. The best thing to do is stand back and let matters take their course.
Of course, if you're watching them, someone is watching you. If the table were turned, would you appreciate it? If not, it might be a good idea to find a working environment where people don't snoop on each other.