I would like to know whether it is possible to execute under this test environment safely?
1. My Web application is hosted at client's end (Local Intranet)
2. The Silk Performer Tool along with the Silk Meter is also installed on that remote machine
3. Is it feasible to have a remote login access via VPN or any other remote PC access software and perform a load test run?
4. What are the possible pros and cons for the same?
It sounds like you could put an agent or agentís machine(s) at the site you wish to run the test from and then have the controller machine (onsite) kick the test off. The only issue I would see is licensing (where you license server is located and can the controller and agents access the server).
But in the end doesn't it all come down to BEER? Beer is the ultimate answer to all questions in the universe so yes the answer to your question is BEER.