Assuming that the mail server is not secured (open relay), you can never be sure whether it will really accept relayed emails or not because they could be accepted but were (dumped) discarded instead without your knowledge and the only way to be sure is to relay an email back to yourself.

Open relays are easily detected by ISP mail serves filtering the BCC: field, which is the most favored method used by spammers to send hundreds (millions) of thousands emails with just one email message--otherwise they will have to send each email one by one, addressing each recipient by the To: field and having to maintain their own expensive high speed mail servers that would limit their spamming activities.

Important:
SMTP Relay Checker probe tools--freeware available from SamSpade.org -- usually trigger an intruder alarm that will alert the IT system administrator of a hacker probing (which is illegal) your IP address, date and time of probe will all be automatically recorded and you can be subject to law suits.

It doesn't matter whether you are trying to be nice to the mail server administrator telling them that their mail server are open relay after you have "probe" them, it is still illegal to do it but if you really want to do probe--it is best to seek written permission first.

Otherwise it's best not to probe anyone's mail server without permission.