If I build some links pointing to http://seaotters.co/post-sitemap1.xml for example will this encourage Googlebot to index more pages?
Generally speaking, no. If it was a HTML sitemap, you could argue you were building link juice to your HTML sitemap which then could be passed on. But for XML sitemaps, no, it is a waste linking to it.
Sure, the site map should help to index your site in fast. Site map is best way to cash your site by Google or Other Search Engine.
No, building links to your sitemap does not encourage Google to index more pages. Having a sitemap is good to tell Google where to "start" looking, but not much else you can do with them. Best you can do is include more pages in the sitemap itself.