I would like to have some checks done upon registration form submition.

These checks compare the value of two fields inorder to verify that they are following some rules.

Example: the two fields are an email address and a company name, and I want to verify that the email address belong to the specific company...

Is it possible to do it with CB, and if YES so, how?

You need to make a plugin. There is an example of this kind of validation in the plugin api documentation.

mikko