For those interested, here's the reply I received from support:
- Show quoted text -
Your registration period will still stay the same but it will have an
DreamHost Support Team + email@example.com
Earn over $97 for each referral: http://www.dreamhost.com/rewards.html
To continue this support case, just reply to this email.
Open a new case at: https://panel.dreamhost.com/?tab=support