Personally I don't use silent mode, because I want to know what is going on with my system.
If you are regularly getting these infected emails, so as to be intrusive and not wanting to be notified about them, perhaps it is time to review your PC security. Rather than treat the symptoms, treat the disease. You can intercept these emails at source (your isp/services mail server) and delete them there, rather than download them.
I use MailWasher Pro, although it is primarily for Spam it is also easy to deal with suspicious emails. There is a free version, but this only works with a single email account. The Pro version works with multiple accounts. There are other options for checking email at source and deleting the spam or suspect email at source, the email server, you don't have to download it.