Yes. We have had people deploy apps that get 500 concurrent connections using only half of a server’s capacity. However, performance varies by the application and its computations. If you are running a Markov Chain Monte Carlo simulation, you could take up an entire server with one user, so it is hard to have a single rule of thumb that applies across the board.
What you want is the right amount of CPU, # of R processes, and RAM for the kind and quantity of applications you deploy. With Shiny Server Pro you can configure all of these settings and see how the performance of your application fluctuates under load. We high recommend you download an evaluation copy and put it through its paces while you tune the settings for your situation.