I don't think so, because both losses were due to bad management decisions under irrational political pressure, not any lack of engineering knowledge that more unmanned testing could have provided.
Challenger was lost because NASA ignored a critical flight risk with the SRB joint O-rings. And by "ignored", I mean "documented that the risk existed, that it could result in loss of vehicle and loss of lives of the crew, and then waived the risk so the Shuttle could keep flying instead of being grounded until the issue was fixed". They didn't need more unmanned testing to find the issue; they needed to stop ignoring it. But that was politically unacceptable since it would have meant grounding the Shuttle until the issue was fixed.
Columbia was lost because NASA ignored the risks of tile damage due to their belief that it couldn't be fixed anyway once the Shuttle was in orbit. But that meant NASA also devoted no effort to eliminating the risk of tile damage by fixing the issue that caused it. Which again would have been politically unacceptable since it would have meant grounding the Shuttle until the issue was fixed.
> They didn't need more unmanned testing to find the issue; they needed to stop ignoring it.
Should such testing have been needed? No.
Was such testing needed, given NASA's political pressures and management? Maybe. Unmanned testing in similar conditions before putting humans on it might've resulted in a nice explosion without loss of life that would've been much harder to ignore than "the hypothesizing of those worrywart engineers," and might've provided the necessary ammunition to resist said political pressures.
Wrong. Both were lost because of a fundamentally BAD ARCHITECTURE. And that architecture was bad because the NASA engineers who designed it, had never designed anything like it before and were never able to test or evaluate any of their assumptions.
Columbia would not have been lost if the Shuttle was top stacked, instead of side stacked.
Challenger would not have been lost if not for the use of solid rockets to launch humans.
Both of these design decisions were done to reduce development effort.