yes but if you're literally never in position to block a shot you will never block shots regardless if you're being dominated in possesion or dominating possesion.
and in the case of brady he's had some of the worst blocked shots rates of any senator in the last 10 years. like historically low. when that stat goes up and you visually see brady playing a more defensively conscious game, blowing the zone less often, it means something.
i don't put too much emphasis in blocked shots either but extreme outliers means something as well doubling your total/60.
clearly something changed.
I think when you're dealing with a 10 or 20 game sample, it's best not to read anything into blocked shots, it's a relatively rare event that can get skewed pretty quick, it's also not indicative of any one thing, so again, it might mean what you're suggesting, or that might be confirmation bias and it's not at all what happened in those games.
I'd also bring it back to the original claim that the defensive effort improved, and that's backed up by the stats, well, is not blowing the zone a defensive effort, or a coaching adjustment? If he's been asked to hang high by the coach, and more recently told they want him deeper in the zone, it's not an effort issue, it's a systems issue.
Anyways, I don't want to get hung up on this, there are some defensive metrics that seem to be better, others that aren't, so I wouldn't feel comfortable saying the stats show he's improved, heck, the two biggest changes are probably on ice Sh% and on ice Sv%, neither tends to strongly correlate with a single skater's level of play, but almost always leads to wins.