Yes! But like all computers it's not formally turing complete because a turing machine is a theoretical computer whose definition requires it to have infinite memory -- and no real computer has that, certainly not the STU-1

Computer designers generally try to get "close enough" by giving their computers large enough memory that no one knows how to use it all... But somehow every few years devs find ways to use it all up and so designers need to make computers with even more memory

Btw the STU-1 doesn't even try on this front, having only 16 bytes of memory. Maybe the STU-2 will have more