Does WordPress default CSS have Grids?

WordPress does not have a default grid framework in CSS. If you are interested in using CSS Grid or another grid framework, perhaps Susy, then do so and have your plugin write specific IDs and classes that are unique.

Looking at the Visual Composer intro video it appears that they are(must be) using specific IDs and classes for the content that is created with the plugin.

This so that in fact it does not conflict with the current theme. Imagine you use Bootstrap for the generated code of your plugin and someone is using a theme based on Bootstrap.

So whatever you do, make sure that the content your plugin creates, the IDs and classes it makes, is unique. Perhaps even use JS to add random numbers to your classes and IDs to make sure they are unique. That would also mean CSS creation for those unique IDs and classes.