Add end-to-end test for custom email

What does this MR do?

Closes gitlab-org/quality/testcases#84 (closed).

More details in the commit messages.

Backport MR: https://gitlab.com/gitlab-org/gitlab-ce/merge_requests/32451.

Does this MR meet the acceptance criteria?

Conformity

• [-] Changelog entry
• [-] Documentation created/updated or follow-up review issue created
• Code review guidelines
• Merge request performance guidelines
• Style guides
• [-] Database guides
• Separation of EE specific content