Yes, actually. Here's an example, probably the best natural experiment we're going to see in this context. Five times more, depending on your idea of "order of magnitude".
https://www.cnn.com/2020/04/28/europe/sweden-coronavirus-loc...
https://www.cnn.com/2020/04/28/europe/sweden-coronavirus-loc...
Even if we take Sweden's case at face value this is still 1/4 the multiplier that people seem to think it is. Furthermore, Sweden is pursuing a strategy of herd immunity: let people get infected so that the populace becomes immune. They should see a higher rise in deaths, but also a faster decline as the virus runs out of viable hosts. A tall, narrow spike versus a wide, shorter curve. The area under the final curve is what we're looking for.
Comparing to its geographical and cultural neighbors helps deal with differences in city structure, public health system, trust in government, population density, etc.