Yes. Each mailbox has a set size from your plan: 5 GB each on Simple and on the Business 5 GB options, and 10 GB each on the Business 10 GB options. Starter has no email. If a mailbox fills up, move to a larger mail option. Adding site disk does not change mailbox size. A full mailbox is a mail upgrade, not a site-disk problem. See Hosting plans: Starter, Simple, and Business for each plan’s mail options.
Related: Create your first email account, Email not arriving? What to check
