#Yes

According to a paper published in Hormones and Behavior by Janice M. Hassett, Erin R. Siebert, and Kim Wallen (citations elided):

Toy play is one of the most robust human behavioral sex differences, showing moderate to very large effect sizes. [Boys] interact more with masculine-type toys than do girls, and girls interact more with feminine-type toys than do boys. Within each sex, boys typically show strong preferences for stereotypically masculine toys, while girls often do not show a statistically greater preference for one toy type over another. Thus sex differences in toy preferences are characterized by stronger gender-specific preferences in boys than in girls.

Socialization does represent one hypothesis for this preference. If correct, it suggests that people in my twins' life influenced (perhaps incidentally) my son to chose balls, not dolls. But the study suggests another possibility:

In contrast to the socialization perspective this view posits that toy preferences reflect preferences for specific activities, such as active manipulation or cradling, facilitated by specific features of toys and that these activity biases result from the different prenatal hormonal environments of boys and girls. According to this perspective, boys’ and girls’ toy preferences reflect differences in their preference for specific activities and they thus seek out toys that facilitate those preferred activities. The “pink” and “blue” aisles in toy stores thus reflect marked gender preferences for activities and not necessarily societal imposition of gender norms on boys and girls. The socialization and activity bias viewpoints do not resolve the sex differences in the magnitude of the preference for gender specific toys. The more marked preference in boys than girls could reflect either that boys have stronger predispositions to a more limited set of activities, or alternatively that boys’ toy choices are more strongly socially constrained than are girls’ choices.

The study examined the activity preference hypothesis by testing the preferences of juvenile rhesus monkeys. They provided the group with the choice of one plush and one wheeled toy¹ to play with for 25 minutes. As with studies of human children, males strongly prefered "boy's toys" and females showed no strong preference. Since these primates do not have strong sexual differentiation in socialization², the authors propose that masculine toys accommodate masculine activity.

In our children, we can't eliminate social pressures, but the research suggests a biological explanation. Androgen has been shown to influence activity preferences: boys like rough and tumble play. Therefore boys will seek objects that afford that sort of activity. Confirming the connection, it's been shown that human girls with "elevated prenatal adrenal androgen secretion" also prefer masculine toys.

Now that my son has shown a preference for balls, my mother-in-law encourages him in his throwing activities. So, at least in my experience, socialization helps solidify preferences, but doesn't introduce them. Observations of my daughter suggest that she prefers quieter play, as a rule. We put plush toys in their cribs and invariably the boy tosses them over the edge and his sister will be clutching something (usually a blanket). So again, when socialization is removed from the equation, my twins turn out to have very stereotypical behavior.

1. The seven plush toys were: Winnie-the-Pooh™, Raggedy-Ann™, a koala bear hand puppet, an armadillo, a teddy bear, Scooby-Doo™, and a turtle. The sizes ranged in length from about 14 cm to 73 cm. The six wheeled toys were: a wagon, a truck, a car, a construction vehicle, a shopping cart, and a dump truck. These ranged in length from 16 to 46 cm. Plush and wheeled toys varied considerably in shape and color as well.

2. Monkeys live in a socially complex world with substantial maternal support, but differential maternal treatment of males and females is limited to maternal retrieval in response to infant distress and physical inspection of their infant’s genitals (Wallen, 2005). Sex differences in maternal treatment do not include preventing their male or female offspring from engaging in opposite-sex typed behavior or in encouraging them to interact with specific objects (Wallen, 2005).