Well, we are close to capability to ignore biological sex when it comes to reproduction. We probably don't/won't want to ignore it, but if we had to, then we most likely could make do with artificial means of reproduction that don't neccessarily need both sexes.
If we're talking about a chromosome going away quickly, then "quickly" in that context means at least thousands of generations. We're not there, but it's not that far away.
Oh, I agree, and research down that line is worth pursuing, but until we're at that point and Y is still important. The implications would be staggering, and no doubt mostly for the better. It could open up the ability to have children to so many couples who currently have few options, be they same sex, infertile, or whatever. The primary downside I can see in the short term is the effect it would likely have on adoptions.
That said, part of me would prefer is we didn't need to rely on non-built-in means to propagate. The idea of becoming utterly reliable on a particular piece of technology for our survival as a species isn't one I'm fond of.