Hi fire,
AdwCleaner is adwanced - automated tool that scans only known adware, toolbars, BHO & registry related, some hijacker shortcuts (malware related) …etc.
Antivirus software usually flags thouse as PUP (Potentially Unwanted Programs) because they really not malicious. They can be removed with their own uninstaller.
Here you may read more about this tool.
http://www.bleepingcomputer.com/download/adwcleaner/
This tool is not designed to search malware. It can’t replace antivirus or security software.
I do not see real need for user to use AdwC for various system scans checks but if you want, I do not see problem why not. Yes you may.
Please note that this tool works on knowly bases, and delete entries according to him known bases. FP are possible.
avast! AntiVirus has his own browser cleaning tool integrated in v8
CCleaner ( orig. CrapCleare ) is registry and temp cleaning tool. They are not related by nature.