Yes, links to your homepage and your interior pages will help the authority of the other pages and, if they're optimized well, can help with their rankings as well. Good links to a page of a website does a positive effect on all other pages.
I am missing something here though--what is the purpose of your "core targeted page"? "I'm wondering if 1-2 additional internal links from blog posts a month is really going to be enough?"
Enough for what?