This happens from time to time. Especially when using plastic syringes to feed. The plastic almost always passes with no real I'll effect. I wouldnt try to induce vomiting at all. If it was too big to swallow, the dragon will likely throw it back up himself. If not, it should travel right on out the other side.
I know it's scary but it will be sharp coming back up too.
The only option you really have is to let it pass, or do exploratory surgery, which would be even riskier than just letting it work it's way out. A small piece of plastic like that wouldnt show up in an xray, so a vet would have to get extremely lucky with their first incision into the GIT, or, there is going to be a lot more damage done at the hands of a scalpel.
This happens from time to time and so far I haven't heard of one case where any real harm came to the dragon. We probably get something like this happening once every other month here.
Just watch for potential blood in the poo and general sickly behavior. but really like I said, this isnt too uncommon, it's just scary when it happens