I've seen this come up a few times - we know that score effects have a real impact on shot differential, and there's an assumption that score effects must also play a significant role in driving team shooting percentage. Let's first look at home team Fenwick% vs score and time elapsed:
This effect shows up most strongly in the third period, particularly the last two minutes of the game. Shooting percentage, on the other hand, doesn't show the same clean trends aside from a massive increase late in the game when a team is shooting on an empty net:
To evaluate the impact score effects have on expected shooting percentage, I looked at each team's home and road shots for from two goals down to two goals up, and assigned them each the league average shooting percentage in these situations. I then compared the spread of this 'average' shooting percentage to the actual spread:
What does that mean? Score effects account for approximately 1.2% of the variation in team even-strength shooting percentage. This is significantly less than the 70% due to luck or the almost 30% due to other factors like shooting talent, shot quality and scorer bias. (The 2005-06 Ottawa Senators had the highest expected shooting percentage, while the 2007-08 Atlanta Thrashers were the worst.) Simply put, while shooting percentage varies by score, score effects have only a negligible impact on team shooting percentage over the course of a season.