No, promo-codes are only valid for new customers purchasing their first plan from DreamHost.
The new domain is unlikely to be on the same IP as your previous domain, but it may (or may not) be within the same IP block.
For example, the 3 of my domains hosted on DreamHost (on the same server and under the same plan) resolve to the following IP addresses;
So of the three, two are in the same block.
In my experience, sub-domains will also tend to be on different IPs. So you may not need to register different top level domains for your SEO requirements.
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