I haven't watched Clarkson enough to comment specifically on how often he shoots, but I agree with your conclusion - if you had a player who was prone to taking additional shots (at the expense of quality shots), I'd expect them to be rated (too) highly by Corsi.
Scott Gomez being the token example of this.
A quick check on stats.hockey-analysis.com says that from 2007-2013 there have been 99 players that have logged 5,000 or more minutes.
He has the lowest percentage of goals on corsi events of any of them, by a decent margin. He's at 3.37% and the next lowest is at 3.52% with only 8 players below 4% Most corsi analysis show Gomez being a decent player. Most people who watch hockey, or even look at goal based metrics, know that simply isn't true any more (and hasn't been for years).
Random note: Average of all those players is 4.714%, the best is Marty St. Louis at 5.72% Crosby misses the 5,000 minute mark, having only played ~4,450 due to his injuries, but posts a 6.4%
Now lets look at Clarkson. I've watched a ton of him playing in Toronto and he certainly seems to fit the mold of throw everything at the net, but I really can't be sure if that's because he's snakebitten and trying to compensate or if that's just the way he is.
I didn't watch a ton of him in New Jersey to judge, but we do have access to numbers courtesy of stats.hockey-analysis.com. Obviously we're dealing with numbers including teammates so it muddies the water a bit, but if the claim is that Clarkson takes a lot of low percentage shots, his CSh% should be low unless he's been paired with guys who are particularly good in that respect.
For the entire 2007-2013 stretch Clarkson played 4920 minutes and had a CF20 of 16.035 and a CA20 of 14.953 meaning he was generating a good number of shots, however is CSh% was only 4.08% That's 156th out of 197 forwards with more than 4000 minutes played.
Lets see if the claim that he's improving his corsi at the expense of quality (trading quantity for quality) bears weight though. If he wasn't, we'd expect these numbers to be roughly the same in the first 3 years of this stretch as well as the last 3. If he is, we'd expect to see a higher CSh% and lower corsi in the first half compared to the second.
So from 2007-2010 Clarkson played ~2,297 minutes. During that time he had a CF20 of 15.251 and a CA20 of 15.730 (CF% 49.2, 164 out of 239) while posting a CSh% of 5.02% (60th out of 239 forwards with >2000 mins played)
From 2010-2013 Clarkson played ~2,623 minutes. During that time he had a CF20 of 16.721 and a CA20 of 14.273 (CF% 53.9, 36 out of 228) while posting a CSh% of 3.33% (216th out of 228 forwards with >2000 mins played)
So yea, it certainly seems like he's changed his corsi approach, going from low numbers but high conversion rate to high numbers but low conversion rate. Granted I didn't review anything about deployment or quality of teammates or competition, but the results are still pretty striking.