I work at a large emergency and specialty Animal hospital in the north east. We get owner permission to include their animals in certain studies and collect samples from animals that fit certain criteria. Some oncology studies automatically obtain data/statistics and many breeders submit or are requested to submit trends they see in their litters. Currently, BIO- bank (through Cornell) runs a number of different studies and collects data from single samples. This means that one vial of blood collected and submitted from one animal can be used in a number of different studies. Shelter and owned animals that are volunteered as blood donors are frequently signed up to participate in other studies. Everything from skin tissue, blood, serum, intestinal biopsies, stool, urine, saliva, etc., can be and/or are collected for a variety of tests and studies. Animals that are euthanized in shelters, or strays that pass in hospitals are often donated. One of our dentists had 4 severed heads in our freezer for months that he used to practice skills on. Additionally, there are breeding/animal labs that do breed excessively to generate sample pools but i try not to think about those. These breeding labs use mice, dogs, pig, rabbits, cats, snakes, etc. The numbers are in the hundreds of thousands (millions for rodent and insect studies).
Apes and other primates are less frequent lab animals and but are still bred for study or volunteered from zoo populations. So yes to your primary question: they do raise thousands and generate captive sample pools, however primates are not as frequently bred or used as lab animals any more. Many are trap-and-release populations but that is not that majority.