I know for a fact they have shipped things out to me on Friday on a number of occasions. I've even gotten items on Saturday after ordering one day shipping on Friday depending on who they used to ship.
They absolutely will ship on Friday, depending on the time. Saturdays and Sundays are much more rare. I think I have seen a total of one order ship on a Saturday, out of all my Amazon orders (which are actually quite a lot). So while it can happen, it's rare, and regardless, they do not count weekends in their shipping time estimates. It's business days only.
"How do I get rid of a Trojan Horse?" -Sailor_Kakashi "Leave it outside the gates of Troy overnight." -Davel23