The numerator is unaffected by testing. When you die, you die, you can’t hide it and can’t hide the cause. If anything, testing may slightly decrease the numerator as at risk individuals may get treatment sooner.
The numerator is underestimated in a way separate from testing. People don't die immediately after they're diagnosed. They die some time after, during which the number of cases increases. Since the naive CFR is just the total number of deaths divided by the total number infected (assuming perfect knowledge of both -- the latter is also underestimated, for reasons you mentioned), this will always underestimate the true CFR until the spread reaches a steady state.
