Hi

No your previous education doesn't go invalid when you do any course or degree from an open school or university. Many people do this. Working people often go for distance education to simultaneously upgrade their knowledge while working to get promoted. This doesn't mean their previous degree goes invalid. If you are going to do home science from NIOS you will have an additional qualification apart from being an arts graduate. They also have something called dual programme and part credit

Under this scheme if you are a learner who

1. is studying in a regular school, or
2. has already passed Secondary Sr. Secondary or any other higher course from any Board/University, you can opt any subjects of your choicse, to update knowledge and educational qualifications

However, on passing, only the statement of grades will be issued, No other certificate will be issued in this case.

I repeat your arts graduate marksheet will not go invalid,you can do NIOS HS without any worry

Hope this answers your query!