This is possible, you can use a Control Adaptor to override the edit mode rendering of the PropertyImageUrl control.
There's an example here: http://sdk.episerver.com/library/cms6/Developers%20Guide/Core%20Features/Properties/Property%20Types.htm

Thank you, that's a start. In the example they add extra properties, how can i call to one of the properties (the description field) and change the isrequired setting?

I'm sorry, it just struck me that you are talking about the image insertion in the TinyMCE editor and not the EPiServer property PropertyImageUrl.
In that case, I don't know if there's an "elegant" way to do it, but you could probably just add some javascript to the file that has the image plugin (Util\Editor\tinymce\plugins\advimage\image.htm). You could do it as simple as just adding a function that checks if the description is set in the onclick of the submit button.

Yes, I just figured that out myself. And indeed, that works.

Thank you for your help!