Theoretically it would be possible to retrieve the thumbnail though this would require custom development. XF doesn't even natively support Mixcloud so it's unlikely we'd add any code ourselves to make this possible.
The majority of sites - usually whether we directly support them or not - are able to generate thumbnails via the social media metadata that sites make available.
However, Mixcloud doesn't seem to include any reasonable metadata whatsoever.
As a result, people sharing Mixcloud URLs on places like Twitter or Facebook are also not going to display any thumbnails:
With this in mind, and with this being a relatively simple fix for most major websites to implement, you may actually be better trying to speak to Mixcloud support to see if this is on their roadmap.