Not tested of course, but I'd imagine the LinkedIn app would cease to function so long as you were connected to the organization's network either via category or a URL block. My assumption based on my limited knowledge of app development would be that the app needs to communicate with LinkedIn.com domain to function.
If you wanted to truly block the app from even install you would have to be managing the device in SM (or other MDM)
Also, Alemabraho is correct, blocking by category may have unintended consequences of blocking sites included in that category that you DONT want to block. My assumption with the goal of blocking LinkedIn was that other professional networking sites would want to be blocked as well. If you strictly want to block one site, URL blocking is the way to go.
However, with URL blocking, you only block that specific domain and in this example LinkedIn's CDN domain, licdn.com, would not be blocked. (But is included in the Professional Networking Category!)