Every time I've had blood drawn it has taken several minutes and required a number of vials; if order was important it seems that it would be affecting the results of conventional blood testing. For me at least, the actual drawing of the blood is anti-climactic and I experience the most anxiety (with it's concomitant physiological reactions) in advance of the blood being drawn at all. Consequentially, it seems likely that the order doesn't matter significantly.

Furthermore, it's hard to imagine how results could be dramatically altered. How would having a previous finger prick blood test for say glucose level, cholesterol, triglycerides, blood count (CBC), calcium levels, blood urea levels, or the presence of antibodies possibly change the results of a subsequent test?