My professor said this in sort of a "I'm pretty sure" kind of way, after saying there is no evidence that any of them ever chose not to take the vows of monastic life. Is this true or at least a reasonable assumption? She explained that the family unit was more important at the time (the time of Benedict and onward) and individual choice wouldn't have factored into the decision much. I dunno, that just seems a bit unrealistic to me but what do I know.
While I'm here, can I ask how common it was for children of well-off families to be given up as oblates? My professor gave us an example of such a family with 4 children - the eldest son inherited the family's title and land, the eldest daughter was married off with a dowry, while both the younger son and daughter became oblate children. Would this be the normal way of doing things for younger children? What would be the alternative?
Medieval historians are generally resistant to statistics, because we simply have no way of knowing. That said, there is an absolutely knock-out study on child oblation in the early medieval west: Mayke de Jong's In Samuel's Image (1996). This is a much expanded version of her earlier article, "Growing up in a Carolingian Monastery: Magister Hildemar and his Oblates," Journal of Medieval History 9 (1983), 99-128. There's less information available on the east or for the later middle ages.
Monasticism—the creation of communities committed to a holy lifestyle—began to flourish in the west some time after Constantine promulgated the official toleration of Christianity in the early 300s. At some point, Christians began following the example of Old Testament figures such as Hannah, who dedicated her son Samuel to the temple at Shiloh (1 Sam 1:20-22). This practice of oblation was common by the time that Benedict of Nursia wrote his set of monastic rules, ca. 530. In the Rule of Benedict, he included a chapter offering guidance "On the Sons of Nobles and of the Poor Who Are Offered."
This set a precedent for gifting children to the church, and De Jong notes that this practice remained popular in the west well into the 1000s. Only in the 1100s did it become common to offer child oblates a choice to leave the monastic community once they reached an appropriate age of discretion (usually about 16 or 17). Conversely, the eastern church never treated child oblation as a binding agreement. Once an eastern oblate reached the age of discretion, he or she was always offered an opportunity to leave.
In some ways, oblation makes a lot of sense. The church needed people who could read, write, speak, and sing Latin. They needed people who know the Bible and the Church Fathers well enough to quote them verbatim from memory. And there were other uniquely religious industries, such as vellum production and book binding, that could benefit from young apprentices. Given the short life expectancy of 35 during the early middle ages, it was in communities' best interests to ensure that a there were children continuously learning how to sustain these basics of religious life and literary culture.
In other ways, child oblation is highly perplexing. Although there was a community need, what could compel a person to sacrifice his or her child and heir to the church? De Jong argues that most attempts to answer this question reflect either modern priorities (like an economic impulse to maximize the inheritance of an eldest son) or modern prejudice (such as the assumption that medieval people were simply irrational or not as evolved and enlightened as we are). This is a point that could certainly use further study.
With this background in mind, it's possible to offer some answers to your questions (I'll do so in reverse):
How common was child oblation among noble families? It was common during the early middle ages, particularly between about 500 and 900 in the west. We have no demographic basis for knowing how this impacted families, aside from a few interesting examples such as the one you cite. However, much of the ecclesiastical population seems to have been given to the church by their parents. This includes some of the most famous churchmen of the early medieval west, such as the English historian Bede and Charlemagne's tutor Alcuin.
Did most children remain in the church once they became adults? This was always a choice in the east, although it's been understudied. In the west, child oblates were expected to stay in the church. If they fled, the were returned to their monasteries like convicts. Only around 1200 did western oblates receive the option to leave their communities, but by this point, the practice of oblation was beginning to diminish as a whole.
One particularly public case allows rare insight. Around 840, the monk Gottschalk fled his Frankish monastery, claiming that he had been forced to take vows. His old teacher, the famous scholar Hrabanus Maurus, who had himself been an oblate, argued that Gottschalk's oblation was permanent and that he had no grounds to refuse monasticism. A church council sided with Gottschalk and allowed him to repudiate his vows, perhaps because his relationships turned so toxic or perhaps because he wanted to become a priest instead. Regardless, Gottschalk's reflections on this experience of unwanted oblation likely encouraged his later heretical views on predestination, causing the church to rue this very unique exception to the common practices of oblation. But Gottschalk's example also goes to show that even in those very rare cases when oblates decided not to live out a monastic lifestyle, they were still likely confined to careers in the church.