In my book Lashon HaKodesh: History, Holiness, & Hebrew (Mosaica Press, 2015), on page 232 I wrote:
This idea comes up again in another, closely related, discussion.
According to Kabbalah, on each day of the seven-day Sukkos festival,
one of seven historical Jewish forefathers “visits” all the Jews’
sukkos as a spiritual guest known as Ushpizin (...
Short answer: It's complicated, but I'm pretty sure it wouldn't be approved.1
Long answer: The core issue here, I believe, is whether or not a shed, even one termed "Jewish", can actually, halachically, be defined as a real Jew (on what exactly a Jewish shed is, see here, here and here).
A similar question is whether or not an alien can convert. ...
Well by halachma anya there are reishonim (Ritva..) that explain why it's in aramaic because we dont want to invite the demons or angels lest they persecute us. That reason would apply to why we invite the ushpizin in aramaic as well.
(These reishonim hold angels don't understand aramaic. See gemara shabbos 12b)