No sir! The word gnostic is the root of agnostic, and that has all to do with religion--not to do with indifference. Occasionally (rarely), the word agnostic is used to describe a non-committal attitude, but it really doesn't fit in your example sentence. To see why you need to look up the definition of gnostic. From Merriam-Webster:
the thought and practice especially of various cults of late pre-Christian and early Christian centuries distinguished by the conviction that matter is evil and that emancipation comes through gnosis [esoteric knowledge of spiritual truth held by the ancient Gnostics to be essential to salvation]
Now, remember that the prefix "a-" means "without". If you stretch this definition a bit, you can probably understand what a statement like, "He abstained from voting because he felt agnostic on the subject of the candidates' proposed policy changes." In this case, "agnostic" doesn't mean that the speaker doesn't care. It means that the speaker feels a distinct lack of conviction. In other words, that he or she isn't confident in either choice, and the speaker is using the word "agnostic" to explain that the reason he or she isn't voting at all is precisely because he or she isn't on board with either option. Your friend might have said, "I will not make a choice because I am agnostic on the matter," but it would be ridiculous for an every day kind of thing because the choice between A and B is probably not consequential enough in the first place that it would require any kind of conviction or certainty.
You're looking for the word apathy, but it doesn't quite fit in the example sentence. Apathy describes a complete lack of concern. You can feel apathetic on a particular topic, such as religion or the question of how Obama is doing as the President, but apathy isn't the best choice for a simple question because the word apathy is used when the topic being discussed is something about which you seemingly should care.