You will. It will be listed with your other databases in the panel. You will get an email from DH to complete the WP installation. It’s only semi-automated.
The only thing that might have made one-clicks less secure in the past was because there were a lot of themes and plug-ins included that, if you didn’t either keep up with or remove could possibly become security holes.
Also, older pre-3.0 versions of WP wouldn’t necessarily have the latest security additions added (like salts in the config file, for example) after being upgraded.
Since a pretty big outbreak of infected/hacked sites earlier this year, DH has tightened up the one-click installs and gotten rid of a lot of the stuff they used to automatically include.
Just remove anything you aren’t using.