No, it's almost always a problem outside of Moodle.
Inside Moodle, you want to make sure your admin has set up Site Admin > Server> Email > SMTP properly. Also, you want to be sure your user has allowed emails to be sent to the *correct* email address when not logged in Profile > Messaging. Lastly, be sure that cron is set to run frequently, if it is set at all.
Outside Moodle, typical problems are failure to connect to SMTP, the SMTP thinking Moodle is sending spam, the next server after SMTP thinking SMTP is sending spam, the intended receiver's ISP thinking it is spam, the email client thinking it is spam.
Be sure the admin bounce back e-address is real, so you can get any rejects.
It is not uncommon, for example for comcast.net to reject emails from our jhu.edu domain as spam because so many come at once. Typically, comcast holds them for three days and then deletes because they are old.