No, EndeavourOS uses the same repositories as Arch for its Desktop Environments. There is no difference between Budgie on Arch or EndeavourOS.
In fact, there is no difference between any package on Arch and on EndeavourOS, except for the 45 packages that are presently in the endeavouros repo and absent from Arch repos.
And yes, you also install a functional GNOME desktop when you install Budgie on Arch (and EndeavourOS). Dependencies clearly show that, as proven above by @dalto.