This is definitely possible as it relates to the US -
(b) Subject to the conditions and requirements of this paragraph, if
all or a portion of the specification or drawing(s) is inadvertently
omitted from an application, but the application contains a claim
under § 1.55 for priority of a prior-filed foreign application, or a
claim under § 1.78 for the benefit of a prior-filed provisional,
nonprovisional, or international application, that was present on the
filing date of the application, and the inadvertently omitted portion
of the specification or drawing(s) is completely contained in the
prior-filed application, the claim under § 1.55 or § 1.78 shall also
be considered an incorporation by reference of the prior-filed
application as to the inadvertently omitted portion of the
specification or drawing(s).
If the priority claim was not present on the filing day then there must be a petition before the material from the priority document can be amended into the application.