Short answer is yes and no. (yes is processes it, but no it doesn’t store it).
It does not appear to be stored in the database (submitted form data is stored in the _postmeta table) however, it is present at form submission time. It possibly be stored but it can be emailed as part of the notification/confirmation.
In your confirmations that you can send to site admins/users, you can output the IP address of the submitter by using the {other:user_ip} but {system:ip} also seems to output the same IP address.
In your confirmation body if you had the following:
{field:all_fields}
{system:date}
{other:user_ip}`
You would receive an email with all the values enter on the form, the date of submission and the IP address.
If you use the action “Export Data Request”, this adds the users data to WordPress’ personal data export tool, allowing admins to comply with the GDPR and other privacy regulations from the site’s front end. I am assuming here as I’ve not actually done this part, but you would hope that one of the fields passed across is the IP address to allow WordPress data management tool to manage it. However, if the IP is not stored by default, then there is no need to WordPress’s personal data tool to manage it. So my assumption here could be wrong.
If you export the submitted data, there doesn’t appear to be an IP field which as we’ve seen above in the _postmeta table, isn’t stored.
However you could possibly create a hidden field and set its value to {other:user_ip}`which would then allow you to export it with the other user submitted fields. If there isn’t already a plugin/function to do that, you could also add your own filter to achieve the same functionality (the filter adds the users IP to a new value stored with the users submitted entries).
Hope that helps more than confuses.
Regards
Chris