CRM integration with website builders
Most builders support automatic integration out of the box. However, the functionality is quite limited: they don't include duplicate checks, no task creation for the manager, and so on.
If necessary, you can always improve such integration to the required, provided that the constructor allows you to insert your own JS code.
During the whole time we have encountered only one system where you can't insert your own code - it is NetHouse website constructor. Therefore, if you are going to create a site using it, study its capabilities for proper integration with various cloud services.