The Economist now has an (April 3) article on this, discussing the death stats from Bergamo specifically.
Official death tolls for covid-19 may exclude people who died before they could be tested. They also ignore people who succumbed to other causes, perhaps because hospitals had no room to treat them. The latter group has been large in other disasters. For example, when Hurricane Maria struck Puerto Rico in 2017, America recorded only 64 deaths. A study later found that the surge in total deaths was close to 3,000. Many occurred in hospitals that lost power.
Such analysis is not yet possible for nations battling covid-19. The only European country whose total death rate (as calculated by Euromomo, a research group) had spiked by March 20th was Italy. This estimate is based on a group of cities. Unfortunately, Italy does not break down covid-19 deaths by city, precluding a comparison of covid-19 and total deaths in the same area.
However, journalists and scholars have crunched their own numbers. L’Eco di Bergamo, a newspaper, has obtained data from 82 localities in Italy’s Bergamo province. In March these places had 2,420 more deaths than in March 2019. Just 1,140, less than half of the increase, were attributed to covid-19. “The data is the tip of the iceberg,” Giorgio Gori, the mayor of Bergamo’s capital, told L’Eco. “Too many victims are not included in the reports because they die at home.”
(As a side note: until April 3, French reports didn't even include deaths in nursing homes.)
And for the broader context:
Comparable figures can be found across Europe. In Spain El País, a newspaper, has published the results of a study by the government’s health research centre, showing that “excess” deaths in the Castile-La Mancha region were double the number attributed to covid-19. Jean-Marc Manach, a French reporter, has found a similar disparity in the department of Haut-Rhin.
So yes, using more accurate local statistics, the extra deaths do "pop up" in graphs, even for the present level of uncertainty.
And actually EuroMOMO now (April 7) shows excess scores for several more countries:
The fact that Italy and Spain are in "the top" z-scores should be self-explanatory by now.
Since there's a misleading chart (for all countries) posted in another answer below, here some updates on the total excess figures in EuroMOMO (not by country), compared to previous years/seaons:
The downward (post-peak) slope in the last chart for 2020 should be interpreted with caution, for there are extra delays in reports nowadays. Interestingly, on cumulated excess deaths, the data insofar for 2020 is enough to put 2020 above the prior years back to 2016: