Lots of people go to college after being homeschooled (with no brick and mortar schooling at all). Even unschooling (where the parent doesn't do anything formal, just gives the child opportunities and allows them to choose what to learn) is enough to prepare a child for college.
After all, many of the top colleges were founded back when only the wealthy had higher education (or much education at all) and it was common for children to have tutors at home (later, boarding schools for teens and sometimes younger children were also common).
From a simple Google Search, I came up with dozens of links right away. Here are a few excerpts.
The Homeschooler’s Guide to Getting Into College
Top schools including Harvard, MIT, Duke, Yale, and Stanford are all
actively recruiting homeschoolers. These schools don't just grudgingly
accept homeschooled students, they do everything they can to get them
in the door, recognizing that homeschoolers are often better prepared
for college than their brick-and-mortar schooled peers.
Can Homeschoolers Attend College?
Colleges are aware that homeschoolers do not fit the typical student
mold and understand that the components of their application may look
different. Admissions departments are very helpful, and some colleges
(ranging from Princeton to Biola) have even set up special pages for
How Do Colleges Evaluate Homeschooled Students?
Home schooled students looking to attend competitive universities
should take particular care in preparing for their standardized tests,
because test scores are one of the few ways in which admissions
committees can compare them to other students academically...Comparison to similar
students is one of the
primary ways admissions committees weigh the significance of an
individual student’s accomplishments, which makes evaluating home
schooled students particularly tricky. Regardless of the rigor of a
student’s course load, colleges cannot determine academic achievement
using grades alone.
Age is certainly a factor and no college is going to take a small child just because she is brilliant. She has to have a well-rounded education, regardless of the source. Tim B has given some good examples where age is not a dealbreaker.
So, yes, it would be quite rare but possible. Especially in a case where the university might make a specialized curriculum for such a child (to appease the parents and get the donations).
Note: While Universities and Colleges are not quite the same thing, in the U.S. we often use the terms interchangeably.