Did Ernest Rutherford's experiment establish the plum budding model of the atom?
No. The plum pudding model of the atom in which the electrons were supposed to be embedded into a positively charged sphere that constituted the atom was proposed by JJ Thomson, the discoverer of the electron.
He supposed that electrons were embedded into the positive sphere in order to explain charge neutrality of the atom.
Also from his experiments, he found that electrons (negative charges) were the only charges which were emitted by metals in CRTs and never positive charges. Therefore, he supposed that electrons were particle like entities which could be ejected from the atom under suitable conditions. He concluded that electrons were particles and the positive charges which were never emitted were not associated the particles. That's how he arrived at his model.
Lord Rutherford discovered the atomic nucleus and suggested his nuclear model of the atom overthrowing the plum pudding model.