If I try to create link and create new artifact on linking screen, can I create a new artifact and add it to an exisiting module?

I don't think you can do it on the same screen, at least for now. As long as you select a module on that screen, the Create New Artifact option will disappear, which means that this feature can only create a "base artifact". Creating a module artifact is much more than that, as you will create a module artifact, its underlying artifact and also define the context in the module.

If you believe the function is crucial to your business, you should raise an enhancement work item (RFE).