Does Exchange accept relayed mail

http://mxtoolbox.com/diagnostic.aspx

Enter your mail servers public IP address or DNS name.

as far as i can tell, that link just checks to see if my mail server is an open relay...

Look in the EMC under server configuration -> hub transport - receive connectors
check the connector settings.  This should give you more of a clue

hmmm, OK.  if, for example, under EMC > Server Config > Hub Transport > Receive Conn > Permission Groups tab, i leave checked "anonymous users," is this the same as allowing relayed messages to terminate at (be received by) my mail server?  

Or is there an authentication option that specifically addresses relayed messages?

This is an authentication option to allow inbound SMTP to connect to your server.  As defined by the remote server IPs listed.  So yes, "the same as allowing relayed messages to terminate at (be received by) my mail server"

Were you looking for a different option?

I'm sorry, I believe I am looking for a slightly different option, unless I'm really confused.  :)

I don't want to filter by IPs since that seems really tedious.  I just want to check to make sure that incoming messages (from the outside world) originate from a non-relayed server.  For example, if spam-userX finds an open-relay mail server and sends messages to my domain, can or does my Exchange server check the header of spam-userX's message to see it was relayed?

Ok I get you now - it's not a perfect solution but turning on TLS helps a bit - it checks certs for authentication.   Without either an edge transport server configured or some third party filter it gets kinds of scary.

OK, gotcha.  But other than checking for authenticated certs, there's no setting in Exchange that would prevent relayed messages from arriving?