I do not like this method of drawing labs. It is a greatly "Modified" mixing method.
In the mixing method, the clinician takes her syringe and withdraws 5-7 cc, and then IMMEDIATELY reinfuses it. He or she then withdraws again, and then IMMEDIATLY reinfuses the blood again. this is repeated approx. 4 times never detaching the syringe from the line. However, with this procedure, though the blood specimen has not been disconnected from the line via the stopcock, It still has been allowed to SIT TOO LONG and therefore clots have been formed and then the nurse is reinfusing these clots. So, no, this is not approriate.
If one is worried about the patient suffering from Iatrogenic anemia from too many phlebotomy specimens collected, the mixing method is best, but not this modification of it.