Do shots fired before the match starts count towards your end-of-game statistics?
No, I've done this with Roadhog shift (Hook) as I wanted to know if this counted towards the end game statistics.
It appears it doesn't start counting them until the match begins as even though I spammed out the abilities and shooting it would only show the stats after, 100% if I landed it 0% if I missed but 50% if I hit the second shot out of 2 regardless how much I spammed during the prep stage.
Backing up the previous answer, no. I noticed it because your first 5 (well, hopefully 5!) shields as Symmetra won't count if you apply them before the match starts.