Out of the box, JIRA does not have such feature, However, this could be achievable by customization or third-party plugin.
Based on Andy's response on https://community.atlassian.com/t5/Jira-questions/Can-I-allow-users-to-create-accounts-on-Jira-only-if-they-email/qaq-p/328599, it seems like JEMH is able to send an email back to the sender to notification that the user needs to signup to JIRA. For more information on JEMH plugin, please feel free to contact them directly via The Plugin People support.
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