Should Patients Be Informed if a Doctor is Inexperienced in a Certain Procedure?

Sculptra is not for average physician injectors. It requires good understanding of anatomy, volume restoration of upper 1/3 of face, dynamics involved with lifting of skin. While any physician injector must start somewhere, somehow, it should be disclosed especially for paying clientele.

Research in your doctor is very important.  Some companies like Sculptra require training and certification before the company will even sell the product to the doctor.  Other companies sell their products to anyone.  My suggestion would be to talk to other patients about their experience and also be up front and ask the doctor about their experience with each product you are considering.  Good luck.

Sculptra is not dispensed to doctors without hands on training from a professional trainer. Obviously, the more experience the better your chances of a desirable outcome. Not every doctor has the "eye" required for successfully using Sculptra so it's a good idea to ask to see their Sculptra patient results before you make a physician selection.
Most physicians will perform additional hands-on practicing on people in their inner circle who are not patients first. And some physicians are very dedicated and will take additional trainings before moving into their own patient base.
I train here in the U.S. and also internationally and take extra time to ensure that those under my tutelage understand the concepts

how Sculptra behaves
what it can do and what it can't do
how to plan out the stages of Sculptra "re-sculpting"
facial areas to avoid
patient selection (who can benefit and how)

A successful Sculptra result does require a certain level of artistic concept. From time to time a physician I am training will decide it's simply not a skill he or she wishes to pursue. It is a fact - Sculptra does require more time and more attention to detail and facial balance. There are many fine cosmetic dermatologists and surgeons who are wizards with fillers who simply prefer to stay with those products alone.
Sculptra is not injected the same way as traditional fillers. There are nuances as to injection technique, facial compartment considerations (some areas of the face are not suitable for Sculptra injections and these have to be identified) and even patient selection. Not everyone is a good Sculptra candidate and physicians have to be frank with patients who may not respond adequately due to profound volume loss or skin condition.
As to your question about a physician putting in writing that you are their "first"? I can't comment adequately on that question. From an personal standpoint, I would assume a paying patient is never the "first" patient for any new procedure a physician has undertaken. But I know of no requirement that forces them to divulge that information.

Absolutely a patient should  be informed if their physician is inexperienced with any procedure including sculptra. I don't think this needs to be in writing but in form of a discussion. Ideally you are being treated by a physician that you know well and trust and who is an advocate for your health and beauty.

Absolutely!  Always ask your practitioner of their experience.  When possible it would be nice to see example before and after images also.

Absolutely, I inform patients when I am performing a new treatment, Sculptra included.  In fact I ask their permission to be one of the first and generally do not charge them.  I feel that they deserve an experienced Sculptra injector and have the right to decline to be a "first time patient".

I generally would tell a patient if I had not done a procedure before, however I am not sure what the point is to put it in writing. If the patient wanted me to put it in writing it  wouldnt be a problem but I would think of it as a little strange to be honest

While your question is specifically about Sculptra, it really demands a broader answer.
Everyone is familiar with the term the "Practice of Medicine" but few pause to actually think about what it means. When an accountant learns how to perform a particular calculation, the result of that calculation performed over and over again forever into the future will be the same if the data in the calculation are the same. However, for a physician, people are never the same and even if we were, the same intervention in the same person may produce different results.
A physician should be always learning and gaining experience throughout their career. But, just like with anyone else, physicians have different skill levels and learn at different rates. So, the "first time" a particular physician does a procedure, it might be better than someone else who has done it a hundred times.
Just like professional athletes, just because someone is "older" does not necessarily mean that they are "better". And, some physicians, as they age or reach the end of their career, are less aware of new developments or perhaps are not as sharp as they once were. Other physicans are at their "best" as they are ready to retire. So, because medicine IS practice, one must choose someone who is competent and capable, regardless of their experience with a very specific procedure and not necessarily based on age.
With respect to injectables, some physicians are very, very experienced because they have injected many patients. If a new product comes out, the skills learned from injecting other products may be applied to the new product and the physician might "instantly" be able to achieve an excellent result.
For example, would you rather have a physician who is a radiologist (a physician who reads x-rays) that never has any patient contact that goes to a course and starts injecting Sculptra into patients inject you after they have "tried it out" on two dozen other patients OR would you rather have a seasoned cosmetic surgeon that has injected thousands of patients (with other products) have you as their first Sculptra patient? I know (not trying to speak badly about radiology as a subspecialty, of course) that I'd be the first patient done by the cosmetic surgeon!
So, the bottom line is that I would personally inform a patient if they were my first Sculptra patient, but that doesn't mean they will have an inferior result nor does it mean that that's what every physician should or would do. And, while a person should have informed consent about any procedure they agree to, I do not believe that if someone is doing a procedure for the first time the patient needs to be informed "in writing."

Unless they have changed their protocol, Sculptra will not sell their product to anyone who has not undergone hands-on training with another practioner who is experienced. With other injectibles , such as Restylane, Perlane, etc.), techniques are similar enough that if a surgeon is comfortable with one, there should be no problem with the first experience with another product.