If the servlet init() block throws an excpetion , then it wont be able to service any requests , that is certain . Now regarding the reason , from docs we can see
Called by the servlet container to indicate to a servlet that the servlet is being placed into service.
The servlet container calls the init method exactly once after instantiating the servlet. The init method must complete successfully before the servlet can receive any requests.
The servlet container cannot place the servlet into service if the init method
1- Throws a ServletException
2- Does not return within a time period defined by the Web server
So , logicaly if ServletException is thrown from init() block , the servlet was never put into service by the container and thus its unable to service any requests.