I use it on my blog too. As far as I know there is no way to put the code in etsy to get people to sign up. I just created a page on my blog and then I link to that in my Etsy store policies. I also mention it when I email people their patterns.
To create the emails though, I have found a wonderful app that connects right to your Etsy shop so you don't have to upload pictures and stuff to a mailchimp campaign. it takes a bit to get used to how it works, but I have liked it so far!
http://craftmonkeyapp.com/sessionsA little tip though, if you misspell something while using this app. Start a whole new campaign. I tried to edit a misspelling and it looked like it changed, but when the email was sent the misspelling was still there. Other than this quirk, it's a great, easy way to send a campaign.
Cheers!
Rachel