Sure thing!
Actually, it's the other way around - your blog should be first and foremost written for the purpose of sharing information with your visitors, etc. BUT it also serves an excellent purpose of doubling as an
SEO draw. Because it's content that is likely to be fresh and regularly updated the search engines LOVE blogs - but a blog only 'contributes' to your website stats directly when it's actually a part of your URL (ie - installed directly on your site =
www.yoursite.net/yourblogtitle )
When your blog is hosted at WP, or elsewhere like Blogger, etc. it's yourblogtitle.blogspot.com or yourblogtitle.wordpress.com
Your blog won't necessarily be indexed any faster one way or the other, but even if you link to yourblogtitle.wordpress.com from your website's main menu it does not count as a literal part of your website (according to the search engines.)
To clarify - if my blog is literally ON my website then my entire website is going to be indexed relative to the numerous search terms you might find on my blog. If my blog is hosted elsewhere and simply linked to my website then any searches being done that might bring people to my blog will ONLY reflect my blog content.
Does that make sense?
As far as getting more traffic and increasing readership - the best way to do that is to just keep investing time and information into your blog - make it a viable resource with well organized *original* content. As you write more, you naturally incorporate more keywords (bearing in mind that TITLE of any blog post becomes the natural 'page title' for that post - which has even more 'search value' than the text inside the post.). As you naturally incorporate more keywords your blog will turn up more and more often and higher up in relative searches (and this is true no matter where your blog is hosted).
Listing your blog and RSS feed in the blog and RSS directories is another way to help give more 'search weight' to your blog - and also has the effect of sending more readers your way.
The blogosphere is HUGE, not to mention the internet - the *only* true 'edge' that will set your blog apart and ultimately help make it a success is consistent posting of new and original content. By incorporating that content *directly* on your website, you increase the 'search value' of your site by association.