Good question. The answer is yes depending on your aims.
To a Server
However, HTML5 has introduced Web Storage, which allows you to create a database on the clients machine. More information is available at:
This will eventually be supported by Construct, but it will probably only be suitable for save games etc. No server interaction.
Resolving the Server Database Issue
Using AJAX requests, you can POST or GET data on a webpage. You will need a webserver with a database on it. Then you can send commands to the page such as "?score=3342" and the page can interpret the data and save it. So the AJAX acts as the middle man between the client and the database, which is a lot safer.