Of course you can. Do you have access to any client? If you enable IMAP, you can test send/receive via Thunderbird IMAP and use SMTP receivers for submission. Or use OWA.
If you're look for a programatic way to do this with no client, you can use openssl/telnet to test IMAP/SMTPS(TLS) the same way Thunderbird would but via CLI.
For IMAP: https://delog.wordpress.com/2011/05/10/access-imap-server-from-the-command-line-using-openssl/
For SMTP: https://scottlinux.com/2014/06/05/check-for-smtp-tls-from-command-line-with-openssl/
If you're trying to test EWS/RCP-HTTP/MAPI, that's a different story. However, if the mailboxes work with base IMAP/SMTP protocols, you know they'll work with the more involved protocols. If the mailboxes are intended to be accessed from the outside, you can test their connectivity via: https://testconnectivity.microsoft.com/
Else, what are the restrictions of the testing?