Depends on the SQL configuration - there is an option to restrict the max simultaneous connections:
Configure the user connections Server Configuration Option[
^]
But, the max you can have is theoretically 32,767 so 200 shouldn't be a problem, provided the hardware and bandwidth is up to it. In practice, you won't have nearly as many as 200 connections busy at the same time - you can't coordinate the PC's to talk at the exact same time anyway, because Windows is a preemptive multitasking OS, so you have no control over what threads are running across the machine at any specific time.