No, you need some kind of programming language (like PHP) to connect with the database.
However, there are lots of 3rd-party email services that give you simple HTML code to place on your website (an email signup form) which will automatically store the entered email address in their own database. In this way, you can (for example) let people subscribe to your mailing list through your site without you having to do anything, and then when you want to do a mailout, you just log into that 3rd party site, create your email, and it sends out to all the addresses in the database.
Such services include CampaignMonitor and MailChimp.
Of course, this may not be what you are looking for, but I though it was worth mentioning. If you just want a normal contact page (with a contact form) you don't really need to store email addresses in a database anyway, do you? What is your aim here?