Rutherford's Alpha Ray Scattering Experiment & Plum-Pudding Model
First of all, yes, your teacher is right for most of the part but it is not that they will go without any collision. Instead, they will penetrate through the foil like a bullet shot at paper.
It is not that the alpha rays will not be deviated but that if the charge was evenly spread throughout the atom, it would not be able to provide sufficient repulsive forces to wear out the kinetic energy already given to the alpha particles and slow them down. As a result, the alpha particles should have penetrated the atom like a bullet penetrates a sheet of paper.