Yes Why not? There is no hard fast rule that you cant. This more or less will depend upon the institute where you pursue the course. However I think you should have a good base in CS as that would be mostly the advantage to study the course. 

Yes definitely any added course into Artificial intelligence can come handy even after post graduation.

You can take up Course into Machine Learning and Artificial intelligence provided by Coursera with partner collge as Stanford University. the course shall be made available for free if you provided an application for Financial aid.

The course gives practical use cases and latest algorithm widely used in various business cases.
It has been regarded as best course across the world and is Taught by ExGoogle Chief, Andrew Ng.

The course gives indepth coverage of artificial intelligence, Machine to Machine communication, deep neural networks, Unsupervised and supervised learning, Big data Analytics and Real time programming assignments to gain hands on experience plus some short quizzes to clear all fundamentals and make you job ready across IT and Telecom sectors.

Hope this helps ..!!!