I realized that I could've answered my own question just now if I had access to some sort of combat log. So I Googled and I Binged, but found only a forum post that implies there isn't one. However, it also shows the problem of forums: it is dated July 2014, so the info might well be outdated without OP or mods being able to update the posts.
What I've also tried: going through all the Hotkeys to find a related option. The only related one seems to be "Observer > Toggle the Console": CTRL + W. However, in "Try" mode nor when watching a replay did that command do anything at all for me.
The existence of hotslogs.com suggests replays do contain at least some statistics. Perhaps you can view the combat log when opening a replay?
Is there a combat log in HotS?