|Interesting question. I don't believe so, probably because the prime focus of ADWCleaner is browser malware.|
I tried copying a C drive program folder that ADWCleaner reports onto an external drive and it still only reported the copy which was on the C drive. I repeated this with the ADWCleaner download on the external and it gave the same results.
As ADWCleaner looks for different things to Windows Defender it is not unreasonable to expect the latter to find something after ADWCleaner has run. This is why to properly clean a computer you need to run several programs. ADWCleaner and MalwareBytes are usually a very good start.
Let Johnw see the logs as per #3.
Always pop back and let us know the outcome - thanks