I want to create a rule so that certain emails do not generate a desktop alert (the pop-ups that appear bottom-right of the screen).
I know I can globally enable or disable desktop alerts, but is it possible to control it for particular emails?
You could control it via disabling the global desktop alerts, and then having a rule at the bottom of the rules list that displays an alert for every message. The trick is to have a rule higher in the list (ie, runs prior to the desktop alert rule) that handles these certain emails that includes the option to "stop processing more rules" on step 1 of the rule creation wizard.
To disable global desktop alerts, navigate as follows:
File -> Options -> Mail -> Message arrival
Then deselect the 'Display a Desktop Alert' option.
To display alerts for all other emails, Go to your inbox, then select
Rules -> Manage Rules and Alerts -> New Rule
From here, click:
'Apply rule on messages I receive' -> Next -> Next -> 'display a Desktop Alert' -> Finish
Then use the arrows to move the rule to the bottom.