Does wand/staff speed matter for Arch Mages / Evans?

With Evans your spell casting speed is completely independent of your weapon speed and defaults to normal (6). From there, your passive skill in first growth brings it down to fast (4) and your booster brings it down to fastest (2), meaning that Evans attack speed cap with everything with just booster. I don't know all the specifics for the other mage classes, but I assume they work in a similar fashion.