Microsoft finally published a long-overdue KB article explaining why signatures are not added to messages initiated using Send to menus in other applications, the Send to Mail Recipient command in Windows Explorer, or by creating the message programmatically. You also can't do anything in Outlook until the message is either sent or saved and closed.
When you use the send to menu in other applications, your only option is to insert the signature yourself, however you can create your own Send to Mail Recipient shortcuts to use with Windows Explorer that will use your desired signature, stationary, and is not modal. The biggest limitation: you are limited to one attachment with the command and will need to insert or drag additional files to the open message unless you use a script instead. Also, Window's Image resizer tool doesn't come up when you attach images using this method.
See Create a custom Send to... Mail Recipient shortcut in Windows Explorer for more information and instructions to create shortcuts or how to use "Joseph's script" (provided).