I think that you are right - the alpha-synuclein gene probably gets switched on in the bone marrow stem cells which lead to formation of red blood cells and so alpha-synuclein protein ends off inside red blood cells. What (if anything) the function of alpha-synuclein protein is in those cells seems to be unknown. I doubt that alpha-synuclein protein can "escape" from red blood cells.

However, there are a couple of papers which may provide food for thought.

One looked at red blood cells in mice which had had their alpha-synuclein gene removed ("knocked-out"). Their red blood cells were fine but they had lower levels of markers of oxidative stress than the red blood cells of mice in which the alpha-synuclein gene was present; http://www.ncbi.nlm.nih.gov/pubmed/25043722 .

The other one showed that, in the MPTP mouse model of PD, the knock-out mice had higher levels of striatal dopamine compared to mice in which the alpha-synuclein gene was present; http://www.ncbi.nlm.nih.gov/pubmed/15288507 .