Well, the answer is yes and no. Technically you can run OpenStudio on a single CPU core. Though you will find that OpenStudio will run quite slow at times and pages might take more then a few seconds to load.
This is caused by the fact that you can only run one app worker process comfortable per core. With one core and one process serving requests, it means that when the process is busy, all other requests will have to wait.
Imagine the case where someone using a mobile phone using a poor connection tries to load a page with a few images like the list of events. The phone will make one request for the page itself and one for each image. Until all requests are handled, other users will have to wait. However this is in case there is only 1 CPU core and 1 app worker process. With a 2nd CPU core and worker process additional requests can be handled without everyone having to wait on the user with the poor connection. Another benefit is much quicker loading times in general. In many cases a few requests need to be made before a page can be shown. The page itself, style sheets, scripts and images are all separate requests. The more worker processes, the more requests can be handled in concurrently.
Although this isn't true in all cases, for the sake of simplicity you could say that with a single CPU core and app worker process requests are handled one by one, in a serial way and with multiple CPU cores and app worker processes requests can be handled in parallel, greatly reducing loading times of even single pages.