No, it’s very unlikely.
PD is a neurodegenerative disease of the
central nervous system. It occurs when the neuronal architecture in certain regions of the brain start to degenerate.
Antibodies are large proteins and typically do not cross the blood brain barrier from the blood into the brain. There are some exceptions; antibodies can enter the brain via a process known as receptor mediated transport. But this typically not the case for antibodies generated in response to a vaccination. Thus, anti-tetanus toxin antibodies generated after vaccination exert their effect in the
peripheral nervous systems.
Interestingly, I found this paper that describes an effort to generate anti-tetanus toxin antibodies that can enter the CNS:
“Tetanus neurotoxin reaches the CNS by axonal retrograde transport and thus becomes inaccessible to current treatments. A possible strategy to improve current therapy for tetanus disease would be the vectorization of Fab'2 fragments, allowing their delivery into the CNS.”
Transport of cationized anti-tetanus Fab'2 fragments across an in vitro blood-brain barrier model: involvement of the transcytosis pathway
Girod et al. J Neurochem 1999 Nov;73(5):2002-8.
https://pubmed.ncbi.nlm.nih.gov/10537059/
Bear in mind that Fab2 antibody fragments are an artificially generated type of antibody; these are different to the natural antibodies made by our immune systems.