The form is submitted via an ajax call to Salesforce through the Server that hosts the web page your form is located at (it could be on any website). As such, the form doesn't "talk" to the Salesforce database directly. Instead, the data from the form is sent via https/REST to Salesforce from the web site's server. Salesforce then sends it to your Salesforce Org instance where the data is received and processed according to the rules you've configured for Web-To-Lead.
There is no "callback" function that would allow you to send a message back to your form. That would require a custom integration to have your form do validation with your database. All you really need do is to make certain you're removing duplicate leads according to the rules you set up when you configure Web-To-Lead.
You can do other real time validation of fields using JavaScript to validate your form prior to allowing someone to submit the form. You can also do RECAPTCHA integration to validate it's a person and not a bot that's completing the form.
However, connecting to your database for validation isn't a trivial task supported via Web-To-Lead functionality. You'd need a secure REST integration from your web site with Salesforce to query the form's input data to your Lead database, search for matches and compare results returning a true or false, as a validation before allowing the form to submit data to the web site's server (for the send to Salesforce) in order to create the functionality you ask about.