The infection rate relevant insofar as it means the population will approach 100% infection [1],- and subsequent immunity or death - faster than other regions. Densely populated areas like New York will have a sharp spike and sharp decline. Loosely populated areas like Kansas will see a slower, steadier rise but also a slower and steadier decline. Social distancing makes areas behave more like rural areas, by virtue of limiting contact. But the same number of people are going to get infected eventually until herd immunity is achieved.
Faster infection doesn't directly result in higher total fatalities, unless medical care lacks capacity. This is a bigger problem for places like New York where the infection rates did put significant burden on healthcare facilities. On the flip side, places less dense than NYC can go without restrictions and this will not impact the overall health outcomes.
Deaths nation-wide have peaked more than a week ago. Deaths among developed countries have also mostly peaked over the last few weeks. Testing almost always under counts, both by virtue of not counting asymptomatic people, and by delays in forming antibodies in the infected. The latter also affects random studies. New York's 20% indicated infection rate likely means that the infection rate today is approaching the 50% or more required to achieve herd immunity.
1. To be more specific, it's estimated that the virus will spread to 50-70% of people before herd would diminish the ability of the virus to spread much further.