Death rate and level of testing is obviously heavily confounded but there are good reasons to think that high levels of testing would reduce the true death rate (and not just reported death rate).
Catching and diagnosing cases earlier allows for better treatment and monitoring of sick patients.
Also, having better information (in this case, a more accurate picture of who is infected) means that the vulnerable can be more shielded.
If you take it to the extreme (test 100% of the population every day), we could stamp this out in 2-4 weeks max, so testing could be the cure. Whether testing reduces the death rate through these other ways I mentioned, that's speculation for now.