This is a very loaded question and I feel it's more on a case by case basis.

No sex until what point? Forever? Until marriage?

I feel like if you mean no sex ever, not even after marriage, that could definately put a strain on the relationship and may lead to problems. It is pretty much expected for a married couple to have sex, if not to have children then just because that is how the marriage is consummated. (traditionally speaking that is)

However, if you mean before marriage - I think it is possible. A relationship is based on much more than sex and if it is solely based on sex, it isn't much of a relationship, IMO. At some point sex may/will become an issue but if the relationship is sturdy enough, a common ground can be found and an agreement made that satisfies both parties.

I could probably say a lot on the topic though I'm not sure where I'm going with my post at the moment and I'd like to see what others type as well.