They most certainly can, a nurse in a doctor's office may have difficulties, but not a trained phlebotomist. And if that fails, ultrasound will 100% be able to obtain blood. I deal with these issues constantly myself as all my major superficial veins are permanently collapsed and gone, it's annoying for sure.
I'm aware, it was just an exaggeration of how we are quick to justify unknown causes as withdrawals. A better, more applicable example, would be how we can think we're in severe withdrawals when a lot of it is just contributed to being starving or malnourished.
A couple things, if it is withdrawal related, it would be PAWS verus acute withdrawals. A large component and difference between acute withdrawals and post acute withdrawals is just the time frame. By 60 days, your body has completely eliminated the drug long ago, which is the reason for the distinction. It's just a biological and physiological certainty due to the drug's pharmacodynamics.
The other issue is that opioids treat symptoms. Your symptoms of an underlying issue may be minor enough to allow the opioids to allow complete cessation of symptoms, in this case, it's not binary but incredibly complex with many inter-connected variables.
With all that said, it's not impossible to be a post acute withdrawal issue solely, just not an acute withdrawal issue.
Edit: You just said if you forget to take Percocet at night you feel horrible, if you are using opioids recently, then it would be acute withdrawals and that changes everything. I may be missing something here, but if you're taking Percocet, you haven't been clean from opioids for 60 days - or did you just recently start taking them to deal with the symptoms?