Afraid not. While the idea of hyperfocal distance sounds like a magical panacea for all focussing problems - it isn't.
The theory of 'depth of field' and 'hyperfocal distance' depends on the concepts of 'acceptable blur' and 'circle of confusion'.
Your lens can only perfectly focus light from a single plane (for a well-designed rectilinear lens). Light coming from objects in front of, or behind, that plane will be blurred - with the degree of blur becoming greater the further the object is from the plane of focus.
A depth of field calculator (like the one to which you've linked) works by deciding how much blur would be too small to notice on your particular camera (i.e., when it's smaller than the circle of confusion). Objects close enough to the plane of focus will produce 'acceptable blur'. The depth of field extends from the closest of these object to the farthest.
The hyperfocal distance is calculated as the closest distance to enable the depth of field to extend to infinity. Which does sound perfect for astro work (hey, if our subjects aren't at infinity - what is?). But remember, objects at the edge of the depth of field are just barely 'acceptably' blurred - but they're still blurred. And the degree of blurring that seems 'acceptable' when shooting landscapes really doesn't produce a result that's 'acceptable' for the bright points of light we expect to see when shooting stars.
I went through this procedure when I first started to shoot stars. I soon discovered that depth of field and all associated concepts just didn't apply to stars. The only way to get sharp images, without using fancy tools, is to do it manually. The development of LiveView and twisty LCD screen with x10 magnification has made this a lot easier.
Also, my theory as to why these may not seem sharp, is because of the long exposure, the stars slightly move which makes it seems like theyre not "sharp". 
