If I send an iMessage to another persons iCloud email will it appear on their iPhone and desktop? I am concerned about security of the message popping up on other devices than their phone. I am sending from my own iPhone - the iMessage shows delivered but I don't know where it has been delivered to them.
It will appear on all devices switched on & signed into iMessage, that have that email address set as a contactable destination for iMessages.
It is under their control rather than yours.
If, for instance, they have their phone with them but are outside a data reception area [middle of the countryside etc] yet also have their Mac at home running & signed in, it will arrive at the Mac & be shown to you as Delivered [& even as Read if they left Messages open with your view-pane frontmost] - yet they may not actually see it until they get home.