While everyone’s body responds to strength training differently, this is fairly unlikely – though it also depends on how you define “bulky.” If you strength train for several months to years, it may lead to a gradual increase in muscle mass, so it is possible that you might notice you have a bit more visible muscle or “tone” after completing the program or later down the line.
However, the program is designed to emphasize strength over hypertrophy (a type of training for increasing muscle mass), so it’s unlikely that you would see a dramatic increase in muscle mass – particularly in just 12 weeks.
Beyond that, putting on an obvious amount of muscle takes a lot of effort and time. You also need to be eating enough calories / carbs / protein and have some other things in place to build significant muscle. Given that we start to lose muscle as we age, I’d say that any muscle that you can maintain or even gain is a positive thing for quality of life. 😉