It will be possible, but I would use a proper glass polish (I saw some in halfrauds the other day). And plenty of elbow grease.
Prep the screen like the detailing guys prep before polishing, or you will make it worse by dragging grit around with the polish.
In the meantime, try Rain-X. It seems to fill small imperfections and tidies up a tired windscreen. The only pain is having to reapply it every few weeks (depending on the weather it will last longer in the summer).