Of course! Everything is possible in Emacs!
Edit: revised solution
If the collapsed status of the parent is all that you want to preserve, then maybe something like the following would be adequate:
(defun my/org-refile-preserve-collapsed-parent ()
(org-up-heading-safe)
(when (save-excursion
(end-of-line)
(org-invisible-p))
(outline-hide-subtree)))
(add-hook 'org-after-refile-insert-hook #'my/org-refile-preserve-collapsed-parent)
original solution
The easiest solution would probably be just to advise org-paste-subtree
(this doesn't quite work):
(defun my-advice/org-save-outline-visibility (orig-fun &rest args)
(org-save-outline-visibility t
(apply orig-fun args)))
(advice-add 'org-paste-subtree :around #'my-advice/org-save-outline-visibility)
If you don't want to have permanent advice on org-paste-subtree
you could advise org-refile
that adds and removes the advice for org-paste-subtree
.