The answer yo your question is always going to be, "It depends!" I've seen "home office business" defined is so many different ways, it's almost been laughable. So if you're talking about working at home, and you set up an 'office' in one room for your computer, printer and telephone, and all you do is telecommuting, then I can see no reason for the HOA to ever have any reason to be concerned. If , however, your "home office business" includes a lot of retail traffic to your home, commercial vehicles parked on your property, driveway and neighborhood streets, or other excessive sound or sight nuisances to your neighbors, then you might very well be inviting the wrath of the HOA Gods.
As a general rule, HOA's and CC&R's are designed to protect and enhance your privacy and right to peaceful enjoyment of your own property without infringing on your neighbors' rights to peaceful enjoyment of their property. If your "home office business" can even remotely jeopardize that concept, then I would encourage you to work with your Buyer's Agent in checking with the specific HOA of any community in which you're thinking of buying a home.
By the way, the property about which you inquired is NOT currently on the market. Once again, an experienced Buyer's Broker Realtor can be of tremendous assistance to you in providing you with current, up-to-date information about homes in your preferred search area and price range.
All the best to you!