I was to have good links to my index page would this count for anything for search engine ranking with other pages on my site?
if you mean that the internal pages of your website linking to your homepage then this in itself will serve your site better for backlinks and navigation.
No, I mean backlinks are there to build SEO on a website. If I have, say, 1,000 links to my home page, this, presumably, will positively affect my home page ranking. But does this carry any weight with other pages on my site - for instance, a page with different contents and different keywords?
OK the way that I look at this is that if you post ot ezinearticles then you are on their home page and Google will then see it as a hi reputation articles. After a few days you will drop off of the home page at ezinearticles and your articles will in Googles eyes look less interesting quality-wise/ So yes home page links will help and the links of those going back to the rest of yoour pages will be good but to a much lesser egree with so many links on a page