98%+ time such kind of Malware goes undetected and unnoticed. It may have effected and corrupted the files which you are not using currently so one wouldn't even know that there is a Malware in that package and would copy it to the external storage.If you just randomly have it connected all the time, or if you reconnect it without first fixing the actual malware problem...then yes, your backup might also get screwed up.
Don't do that.
My nightly imaging to the NAS might be affected.
The weekly backup internally in the NAS won't. The PCs know nothing about it.
Only accessible if logged on to the actual NAS.
The weekly backup will also be affected.
Seriously if a Malware is able to avoid being detected by Anti Virus Software then what chance does a person stand on checking or tracking it. Because all the instantaneous triggering or noticeable malware can easily be avoided by Anti Virus Software like Kaspersky or Bit-fender. In that case again the Storage being Internal vs External or being backed up daily or once a weak won't matter much.