Chelation-Therapy is not used to treat the ingestion of plastic, but rather metals. The chelation mixture is given to the bird and it basically attaches to/coats the metal that is throughout his GI Tract, which keeps the metal from being absorbed into his bloodstream and poisoning him. Then the metal is eventually excreted in the bird's poop, as the chelation mixture is able to be excreted normally, like food is, through the GI Tract and out of his intestines, and since it's attached to the metal, it carries the metal out with it, and it keeps it coated so that none of the metal is able to get "loose" and be absorbed into his bloodstream at any point on the way out...
If he ate plastic then this would not "poison" him at all, but rather pose a risk in perforating his GI Tract somewhere along it's journey out of his body, or if the piece of plastic is too large to pass through his GI Tract and out in his feces then that's another issue, as is the possibility that the plastic may have a sharp, jagged piece that could cause an internal injury and internal bleeding. Heavy Metals are not able to travel though the GI Tract and be excreted in the feces, if they are ingested they simply sit inside of the bird's stomach, literally forever, or until enough of the metal is absorbed into the bloodstream that it poisons and kills the bird...Plastic can and will be carried out of the body through the GI Tract, sometimes safely and without any issue...So these are two very different situations and very different treatments...
Is this Vet a Certified Avian Vet, or is it an "exotics" vet? The reason that I'm asking here is that there's some information missing, I'm hoping it's just a matter of you not mentioning it and it's not that the vet didn't do it...How did the vet go about diagnosing Heavy-Metal Poisoning in the first place before taking blood? I'm hoping that the first thing he did was a regular, flat-panel x-ray, and this is how he diagnosed the heavy-metal poisoning, as metal anywhere inside of his GI Tract will light-up like a Christmas Tree and be easily recognizable without a doubt. However, it sounds like this wasn't actually done, because you're still not sure whether it's metal or plastic that is inside of him, etc., and a simple, plain old x-ray that takes 10 minutes will immediately and definitely tell the vet whether or not it's metal or some other substance inside of his GI Tract (or that there isn't anything inside of him)...
I guess I need more info in order to tell you anything more about this situation, but the biggest question is what were his original symptoms/why did you bring him to the vet in the first place, how long were they going on, and what tests have they run so far on him? I mean, you already said they have yet to do any blood work, so if they also haven't taken an x-ray yet, then they don't even know if the problem is due to something he ate!!! That's what I'm trying to get at...
If they do a regular x-ray then they should be able to tell whether or not the problem is that he ate something in the first place and now it's inside of his GI Tract somewhere, if there is something inside of his GI Tract that he ate whether or not it's metal or some other material, as well as showing any gas/air or fluid/blood in any areas that they shouldn't be, indicating a tear or perforation of the intestinal tract...
****As far as him possibly needing surgery, if the x-ray shows that he did in-fact ingest something and it's inside of his GI Tract, and that it's not made of metal, then it's simply a matter of whether or not he will be able to pass it out in his feces or not, and whether or not it's causing any type of OBSTRUCTION (whether it's plastic, nylon, a collection of fuzz from a toys like one of those killer "Happy Huts/Tents", etc., it doesn't matter, once they confirm that it's NOT metal then it will either pass on it's own or have to be removed, period)....THE X-RAY WILL SHOW THEM THE SIZE OF THE OBJECT, so they should be able to at least tell whether or not it will be able to pass based on it's size, though they probably won't be able to tell what it is or if it's sharp, jagged, etc.
If they inject him with a contrast-solution and then take an x-ray, they'll be able to tell whether or not the object is causing an obstruction, in which case surgery is a must and is not optional (usually they'll become extremely sick with a bowel/GI obstruction, they'll be extremely lethargic and usually vomit, and then stop eating and drinking).
So the answer to your question is that if he did ingest something and it's not metal, then he may be able to simply pass it, or it may need to be removed if it's too large, oddly shaped, sharp/jagged, or if it's causing an obstruction, as chelation only works to pass metal through the GI Tract and out of the body. If it's metal that he ingested then they can give him the chelation-therapy with the hope to eventually have the metal pass safely through the GI Tract and out in his feces without any of it being absorbed into his bloodstream. Usually the chelation-therapy takes quite a while, and it's rough on the bird. It works very well and is very successful, but it does cause the bird to feel quite badly, they tend to be very, very lethargic, sleep a lot, lose their appetites, lose weight throughout the process, and even have nausea and vomiting from the chelation solution...but it saves their life...
***And as already stated, if it is metal that he ingested, it's usually either from them chewing on their cage bars (if they have any coating on them) or eating small pieces of toys, or even chewing-up anything that has metal-threads in it, such as anything with wire (like a power cord, they commonly will chew-through the insulation on power cords and end-up with tiny little wire fragments stuck in their stomach or intestines). And if he has any toys that are made of fabric/cotton/fleece/anything fuzzy, like a rope perch or any type of Happy/Snuggle Hut or Tent, then he could very well have an obstruction if he chews on it, as they eat little bits of the material over time and it accumulates slowly inside their GI Tract until it fully-obstructs their intestines and has to be removed...