If A doctor orders blood work can it be done anytime?
Some blood tests must be done under specific conditions to get valid measurements. For example, you may be asked to fast to measure blood sugar or cholesterol. A lunch just before the test would throw those numbers off. Normally if the test requires anything special you'll get instructions, check the papers you got on the way out. When in doubt call the doctor's office or the lab where you'll be giving samples.
The prescription would clearly point out when and how the blood work ought to be done. Freedom to get it done is yours.
if the lab-technician is in the lab, yes GW is correct that some tests require certain conditions