Can SQL Server Express Send Emails?

I am fiddling around with one of my SQL Server Express instances, and I'm trying to get it to send me an email.  I just read these links.
http://execsql.org/configure-send-database-email-sql-server-2012-express-edition
http://www.databasejournal.com/features/mssql/article.php/3626056/Database-Mail-in-SQL-Server-2005.htm

I followed all the steps there, and now, as I'm trying to send myself an email, I get this message.
The mail could not be sent to the recipients because of the mail server failure. Exception Message: Could not connect to mail server.

When I run this:
SELECT * FROM msdb.dbo.sysmail_event_log;

I see this:
description ...