Yes it you get them at the same time.

I was diagnosed with Parkinson's in July of 2023. My symptoms began 7 years ago and long story short she told us I was in early stage 3 and I would probably be in a wheelchair in 3 to 5 years. At that time I had already had the first, second and third shot. I had also had 2 cases of covid, both were nuthin burgers, a wave of nausea and a headache for about a week. January 12th I was rushed to the ER with a 103° temperature. This was the first of 4 total trips as well as 1 visit to my home by the EMS. I was ill for almost a month. Since then I have had increased symptoms and was told by my doctor that I am now in early stage 4. We just bought a mobility chair because I can no longer walk any distance.
Cause and effect???? We'll see.

Personally my approach is that it is important to avoid getting covid and so far so good knock on wood.
SARS-CoV-2 infection is considered responsible for the development of parkinsonism. However, the mechanism by which COVID-19 triggers neurodegeneration remains to be determined
https://www.ncbi.nlm.nih.gov/pmc/articles/PMC98....

Links between COVID-19 and Parkinson’s disease/Alzheimer’s disease: reciprocal impacts, medical care strategies and underlying mechanisms

https://www.ncbi.nlm.nih.gov/pmc/articles/PMC9885419/

"Although COVID-19 primarily affects the respiratory system, it has been associated with a range of neurological symptoms, including confusion, memory problems and seizures. Furthermore, COVID-19 may contribute to the development of parkinsonian features, including tremor, rigidity and bradykinesia"
https://www.ncbi.nlm.nih.gov/pmc/articles/PMC10....

SARS-CoV-2 and Parkinson’s Disease: A Review of Where We Are Now

https://www.ncbi.nlm.nih.gov/pmc/articles/PMC10526287/

Parkinsons was around long before Covid was thought about.