The Short Version
The evidence strongly indicates that Eoraptor was not a close relative of Tyrannosaurus rex. Recent phylogenetic work usually places Eoraptor outside Theropoda or at most very near its base, far from the derived tyrannosaur lineage. The only meaningful caveat is that the phrase "within theropod dinosaurs" is somewhat imprecise because Eoraptor may not have been a theropod at all.