We can use other countries if you want.
Germany, for example, has a population density 6.5x that of the US.
They've had 212,190 cases and 9,290 deaths. Adjusted for total population (multiply by 4), that's 848,760 cases and 37,160 deaths.
South Korea has a population density twice that of Germany.
They've had 15,515 cases and 305 deaths. Adjusted for total population (multiply by 6.5), that's 100,848 cases and 1,983 deaths.
Clearly, population density does not necessarily correlate with the number of cases. Also, while Canada does have a very low population density, that's primarily because a huge portion of the country is almost entirely uninhabited. The vast majority of its citizens live in a pretty narrow band just north of the US border. Within that area, the population density is pretty similar to the US.