My unofficial answer is no.
I wasn't even aware Z53.20 Procedure and treatment not carried out because of patient's decision for unspecified reasons existed, and I have been coding for quite awhile. To me, many of the Z codes exist, but are not often used in real world coding. If every physician who advised a patient to have a mammogram, or colonoscopy, or cholesterol screening and the patient didn't want to, used this - it would be on 50% of claims.
I would consider using it (now that I know it exists) if the documentation made it seem the patient declined all/most services.
For example: Pt comes in with ovarian cyst. We do a sonogram, some labwork. Nothing jumps out as alarming. Physician states we can remove it surgically or monitor it with another sonogram in 2 months to see if cyst has grown. If the patient chooses to monitor it, I certainly would not put Z53.20 since she declined the surgery.
Similarly, many of the history codes. Who doesn't have history of a fracture?? Sure, if you're treating a patient for osteoporosis and has had 3 recent fractures, it's relevant and go ahead and use it. But a patient declining an "offer" of lumbar puncture seems like a fairly common situation and would not require (again, in my unofficial opinion) Z53.20. You could fill 3 pages of Z codes for every patient.