In Final Cut Pro 10.1 yes - you can choose between 'Managed media' (copied) or 'Referenced media'.
In iMovie 10 I am not aware of any choice.
As far as I can tell, iMovie 10 always makes a copy of your clips when importing directly from a camera or from a file. The only exceptions are for movies that were imported into an iPhoto or iTunes library (maybe other apps too like Aperture) which are then referenced from these libraries provided they are brought into iMovie using the Content Library.
In principle you do not need to keep your source files after importing them but it would be wise to have a backup somewhere, especially since some people are reporting diappearing clips with imovie 10.0.3.
(I wonder whether people who report that they cannot share a movie and receive an error message something like " iMovie is still referencing the camera" have somehow got iMovie choosing to reference rather than copy during import)