Yes, rubber bands obey Hooke's law, but only for small applied forces. This limit depends on its physical properties. This is mainly the cross-section area, as rubber bands with a greater cross-sectional area can bear greater applied forces than those with smaller cross-section areas.
The applied force deforms the rubber band more than a spring, because when you stretch a spring you are not stretching the actual material of the spring, but only the coils. Read more