If all your asp code has all the database calls on the server side, and the server is configured properly with your database credentials, and you've taken appropriate steps to isolate all user-entered values, to sanitize your inputs, to treat data as data and never as sql code, and to secure your website, then all is probably fine.
Depending on how your system is configured you can publish your database along with the site. If it works than it will run, if it doesn't work then you need to set up your server differently. Beware that with that configuration re-publishing your site might overwrite your database.
Unfortunately, in this realm if you have to ask if all is well, the answer is probably 'no'. Or at least, probably that what you have is not secure and not safe to publish.
You might be able to put your data up just fine and you might get results that look good to you, just be aware that 'bad guys' can probably break your site and access everything too.
