Is it possible to drag the preview of a kit into the project as a MIDI file or similar, so that you can use the preview as the basis for your own beat?
Yes, Every Maschine Kit already comes with Patterns (usually multiple patterns) that can be loaded. You can change drag or do whatever you want with the midi of those
On the hardware while Browsing GROUPS for a kit hold "SHIFT" and an option will show up on the left screen... "+PATTERNS" select it and it will load the MIDI for the Patterns you hear in the previews and more.
On the Software select "+Patterns" on the bottom of the browser.