I have only done link building in English although Spanish language searches are also very important. I have seen our SERP improve also for Spanish searches. Is this care of the improved English SERP?
Yes, I think the SEO you do for english will help you with your SEO in spanish. However, there are factors you should consider. If your market is span, you should include "spain" in your metatags and anchor texts, for example. Also, a domain .es willl help you rank well for searches on google.es.