To check this using the premises/query already mentioned in the previous answer, I first checked for the percentage of questions that were closed vs the total of undeleted questions (Intentionally excluding deleted ones to remove the deleted & closed noise). This is what we get when analyzing the first question of each user:
The median for the year before the change (Oct '14 - Oct '15) is 9.25%, with an average of 7.63%. The month with the highest percentage is 11.15% in Sep '15 and the lowest is 4.57% in Oct '14.
A year after the change (Nov 15' - Nov '16) we actually have a higher percentage of closed questions. A median of 11.41%, an average of 11.15% (Same as the highest in the year before!). The highest month is Aug '16 with 14.59% and the minimum is 6.57% in Dec '15.
So we see an overall increase in closed questions - a higher minimum and maximum and an increase in average and median.
Here's a zoom in the percentages:
There is a quite different picture for deleted ones, though. This is what we get when we look at deleted questions for the first question of each user:
The median for the year before the change (Oct '14 - Oct '15) is 36.2%, with an average of 36.2% too. The month with the highest percentage is Sep '15 with 39.26% and the lowest is Jan '15 with 33.17%.
A year after the change (Nov 15' - Nov '16) there's a clear diminish in the percentage of deleted questions. The median is 32.72%, with an average of 33.43%. Nov '16 has the highest with 37.40% and Jun '16 has the lowest with 29.7%.
Here's a zoom in the percentages:
Another thing worth considering is if the tool served as a deterrent for people asking questions, here's the percentage of new users that asked a question on the month they created the account:
There's a noticeable drop from a median of 60.92% and an average of 61.25% to a median of 55.31% and an average of 55.39% after the tool was implemented.
However, from the line in the graph, there seems to be a general decline over time and no significant spike when the tool was implemented - so that's a dead end.
Conclusions
I do not think the date is enough to say with clear certainty that the tool worked or didn't - there are contradictory indications here. One possibility is that it did help, and thus we saw a decline in the number of deleted questions. Though it didn't help that much, because a lot of the questions that would be deleted are still not good enough and thus get closed. It is hard to say that though without looking at the specific close reasons for each question.
One more point of noise is that it seems that October is particularly a busy month on Math, notice the spike in 2014 (not as significant), 2015, 2016 and 2017. And then a rapid fall-off in the following months.
My next suggestion would be looking at Flag Types and see if there's a noticeable change if you folks really want to dig deep into it.
It seems there isn't strong causation of the tool being implemented and an improvement in the quality of questions. There's definitely a correlation that there are less deleted ones after the tool, but causation cannot be proven.