Yes, you can use MailChimp templates in Mandrill. You'll need to push them from your MailChimp account to Mandrill for them to be accessible. This is a one-time push, so if they're updated in MailChimp and you want the Mandrill version to also be updated, you would push it again.
In MailChimp, go to Dashboard > Templates > My Templates. Hover over a template stored in your account and click Send to Mandrill.