The short answer is no. And no, vaccinations of any kind do not cause autism.
This is part of the whole myth about "leaky gut".
First, the evidence, then the myth.
At present, there are no biologically-based tests that can diagnose autism. Not blood tests, not screening tests using biological markers. Nothing.
Can autism be detected by testing for "toxins" in the blood? (And by implication, in the brain?) No. The folk that so proclaim have no evidentiary basis. There are labs that claim to test for autism and other conditions from blood samples and other biological samples. Even Fox News (Fox News!) have condemned them.
The myth runs something like this:
A typically-developing child is vaccinated; the child develops "leaky gut", which allows particles (petides) from food, especially gluten and casein, to leak into the blood. These peptides can cross the blood-brain barrier, because they are similar in structure to natural opioids, so they are a match for structures in the opioid receptors in the brain. Thus, these peptides cause the problems with speech, social skills and behavior that are the hallmarks of autism. If you remove the sources (gluten and casein) from an autistic child's diet, plus adding other treatments, the autism can be reversed.
The most famous person advocating this myth is Jenny McCarthy, who said in a 2007 interview promoting her book:
You know, I could in two months turn Evan completely autistic again. I could do it completely through diet. And maybe getting some vaccine boosters. Through diet, I could load him up again with all the things that will aggravate the damage that was done. Right now, what happened now was that I healed him to the point where he got everything back to this baseline level and it stays there like this. But I mess with it at all–boom!
No. Just no