If you already included the links in your content (on the new and old entry), then you don't need to approve the comments in order to get the benefits of the internal link structure. However, your links are unlikely to look spammy since it will be clear to readers that it's a link from your own blog and most likely a follow up, plus it notifies readers that new content is up and they can follow the link to see it.
In any event, it's up to you which method you choose (i.e. manually updating the old post to include the link to the new one), approving the pingback, or installing a related entries plugin which will hopefully pick up the new entry and display it.
On another note, if you are going with the pingback method, you'll want to disable the rel="nofollow" attribute, otherwise your link will get no Google love in the first place.
~ Teli
