I think so, yes.
For example, on S&H, Cathe does 3 sets of slow bicep curls with dumbells, and 3 sets of hammer curls with dumbells. After that, she does 3 sets of barbell curls. I can keep going and still stay heavy with the barbell curls precisely because we switch to the barbell. After all, by the time I have done the previous 6 sets, my biceps are on their way to being fried. it is the slight change in the way the weight is lifted with the barbell that allows me to continue to lift heavy and keep challenging the muscle.
Also, I can only do about 6-8 reps with 20 pound dumbells, and only when the muscle is fresh. But I can do more than that with a 40 pound barbell.
Since the barbell is useful for training so many muscle groups, why not invest in some more and more varied plates so that you can extend its usefulness to you, since you have already invested in the barbell purchase?
Clare