No, we basically never do that in Japanese culture, which is why it took me and my classmates by surprise to learn, in our English class back in junior high school, about that custom in the English-speaking world.
We would use the actual name or nickname of the son nearly 100% of the time.
The only time that I could think of parents (mostly fathers) addressing their sons as 「息子{むすこ}」 would be in very serious/important letters or poems. In such cases, it would generally be 「息子よ」 instead of just 「息子」.
Even on those occasions, however, many parents would still just use the actual name.