It is indeed possible. You can use the "Transition Linked Issues" post-function, with the "is Parent of" link type, to automatically trigger a particular transition on all subtasks. Of course, you must add the post-function to any transition that applies to parent issues.
As for "all subtasks that do not have a particular status or statuses", I'm not sure I understand what you mean by that. Do you mean that you would like to transition only subtasks that are not in specified statuses? In any case, transitions generally apply to one or more source statuses (they take issues from one or more statuses to a single destination status) so that would basically solve your issue.
David
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