Role of Prevalence in Estimating Coronavirus Mortality
I think you're talking (setting aside false-positive/low-specificity testing problems for the moment) about the difference between infection fatality ratio (IFR, fraction of infected people who die from disease) and the case fatality ratio (CFR, fraction of clinically defined "cases" who die from disease). The difference between these two depends completely, as you suggest, on the difference between the population that gets infected and the population that is defined as a "case" (which could vary a lot: is it people who have a cough? fever &amp; cough? request testing? are admitted to the hospital? are admitted to the ICU?).

Because most of the people aboard the Diamond Princess cruise ship were tested (3063/3711), we can have a reasonably good idea of the fraction infected (unlike the usual scenario where most asymptomatic cases are never noticed). The authors of this (not yet peer-reviewed) study concluded that:


  the all-age cIFR on the Diamond Princess was 1.2% (0.38–2.7%) and the cCFR was 2.3% (0.75–5.3%)


(where 'c' in cIFR and cCFR stands for 'corrected'; these are estimates that account for the fact that we don't yet know the outcome for all patients).

Other issues to think about:


sensitivity and specificity of testing (false positive/negative rates)
variation with/adjustment for age (discussed in the paper)
variation by medical/social context (e.g. Wuhan vs Iran vs places where cases are caught early and the medical infrastructure isn't overwhelmed)




Russell et al., "Estimating the infection and case fatality ratio for COVID-19 using age-adjusted data from the outbreak on the Diamond Princess cruise ship". https://cmmid.github.io/topics/covid19/severity/diamond_cruise_cfr_estimates.html