Dear Mallikarjun,
You have not mentioned whether you applied for any Govt job through State or the Union Public Service Commission or any State or Central Public Sector Undertaking and whether you mentioned anything about your present employment in your application.
Normally, when you are selected for any post through the State/Union Public Service Commission, all your documents would be verified at the initial stage of appointment by the recruitment agency and the department to which you are allotted. There would be verification through the Police about your anecdotes.
Therefore, the point you raised has no relevance to your Govt job if you are selected. When you leave the current private organization, get the relief proper and get experience certificate. That would be necessary in case of back ground verification by any industrial undertaking whether in the private or public sector, if you have mentioned it in your application.