Is the site internal linking structure important?

Absolutely. When a crawler looks at your site it's trying to find out what the most important pages are - it's safe to assume that a page with many internal links to it is probably something you want people to see so the search engines treat it accordingly.

Also, a crawler wants, as quickly as possible, to find all your pages and get them indexed - if you site structure is good and easy to follow then you make the crawlers job easier.

A sitemap can help with this but you really should ensure that your site "flows"...