It shouldn’t. In fact, the only information that I recall providing is an e-mail address (for the account) as a contact if something’s up with the certificates or for stuff like renewal reminders.
If you don’t want to run the whole client, which is a bit overkill for manual stuff, you can look at other community-provided clients listed here. The simplest option listed there is the site https://gethttpsforfree.com/ which takes you through the manual steps to get your certificate.