Is it possible to register an imagelist instance for scripting and use it inside the script?
Yes, it's possible, and you don't need to register, as it's registered by default. If you launch the scripter IDE (for example, the ScripterProIDE demo in "demos\ide" folder), you will see TImageList is available in the component palette.
Is there a possibility to use a TImageList instance available inside the program (a Delphi object, not in the script)?
No, the components in the script form are just like in Delphi: they are "design-time" and whenever you create an instance of the form, instances of the components dropped in it are created. You can use existing ImageList (and any object) from script, but then only from code, at script "runtime".