I don't think so because the month they finish is not related to how long they take. And for live reporting the data output changes this month if for instance next month a very long project finishes.
Split your projects into cohorts based on when they started. Then figure out for each cohort after 1, 2 .. N months, what proportion were completed. Plot those cumulative distributions and compare. If you want to assess significance then you do a chi-squared test.
This still means that if a project is finished in the future, that trend in the past would change. Which I think means that it would work if all of your projects were finished. Could something like a mann kendall test be sensible?
I don't think so because the month they finish is not related to how long they take. And for live reporting the data output changes this month if for instance next month a very long project finishes.