You should really define what you mean by 'running'.
You can get the general status of the server by chucking a JSON request at it.
You see the server will implement the Wire Protocol, so it means that it will, or at least should, respond to the following list of REST url's:
http://code.google.com/p/selenium/wiki/JsonWireProtocol
Specifically:
http://code.google.com/p/selenium/wiki/JsonWireProtocol#/status
and possibly
http://code.google.com/p/selenium/wiki/JsonWireProtocol#GET_/sessions
The status
supposedly, will:
The server should respond with a general "HTTP 200 OK" response if it is alive and accepting commands
If this is what you mean by 'running', that it is alive and kicking and willing to accept commands, then you will need to send off a request to /status
and check for the response you get back.