I missed the 'uni' part, but looking it up there seem to be differing opinions. Young Adults can buy businesses, but some people say the business has to be in the main hood and some say that it can be in a Uni hood. No home businesses in Uni and you can't run one from a dorm, but otherwise IDK.

This is easy to test by choosing the "real estate" option on your phone. When you try to buy a community lot, it will pull up available choices according to hood, just like when you're choosing a community lot to visit, and you can switch subhoods. If community lots can be bought in a university hood, you will be able to choose a university hood and see all lots zoned "community."

I have tried this, and you can no more buy a community lot in a university subhood than you can buy a vacation home in a main hood. Only the main hood, downtown, and any shopping districts will be available to look. But I don't expect anyone to rely on my faulty memory, and heaven knows what somebody may have modded. So by all means test it yourself.