This arborial query come to Zamboni just today.
To this I say most definitely yes. The asker says that her spouse is of non-jewishness and they have children who like to have a tree. It is just a tree with many lights! A tree is a non-denominational little being. There are trees is Israel. In fact, an old Jewish saying says that a man must do three things in his lifetime: have a son, plant a tree, and write a book. Think of this tree in that way. Everyone who plants one is Jew!
And too, a menorah going full force on night number 8 is much like a tree lit up, no?
Zamboni say if your Irish girlfriend Cathy o’Shea can pig out on your aunt Tilly’s latkas, then you can enjoy tree for a month.
I hope this helps, and you can always put Star of David on top.