I figured out that I need to just add the send email code to the python script. I was able to find this help document that pretty much laid out the process for me. I made some minor adjustments and came up with:
import smtplib, time, arcpy, arceditor
#block new connections to the database.
arcpy.AcceptConnections('Database Connections/MyConnection.sde', False)
# wait 5 minutes
time.sleep(300)
# Disconnect all users from the database.
arcpy.DisconnectUser('Database Connections/MyConnection.sde', "ALL")
# Get a list of versions to pass into the ReconcileVersions tool.
versionList = arcpy.ListVersions('Database Connections/MyConnection.sde')
# Execute the ReconcileVersions tool.
arcpy.ReconcileVersions_management('Database Connections/MyConnection.sde', "ALL_VERSIONS", "sde.DEFAULT", versionList, "LOCK_ACQUIRED", "ABORT_CONFLICTS", "BY_OBJECT", "FAVOR_TARGET_VERSION", "POST", "KEEP_VERSION", "c:/path/to/log.txt")
# Run the compress tool.
arcpy.Compress_management('Database Connections/MyConnection.sde')
#Allow the database to begin accepting connections again
arcpy.AcceptConnections('Database Connections/MyConnection.sde', True)
# Get Messages
ScriptMessages = arcpy.GetMessages()
# Send Email when script is complete
SERVER = "mailserver.yourcompany.com"
FROM = "GIS Admin <mail@yourcompany.com>"
TO = "johndoe@yourcompany.com"
SUBJECT = "The Script Has Completed"
MSG = "This is an auto generated Message.\n\rThe Reconcile & Compress script has completed.\n\n" + ScriptMessages
# Prepare actual message
MESSAGE = """\
From: %s
To: %s
Subject: %s
%s
""" % (FROM, ", ".join(TO), SUBJECT, MSG)
# Send the mail
server = smtplib.SMTP(SERVER)
server.sendmail(FROM, TO, MESSAGE)
server.quit()