Not directly. But you can write out the results of your query to a file in your vospace, and then read that file as often as you wish. Example (in a Jupyter notebook):
query = # my query string
result = queryClient.query(token,query,fmt='csv',out='vos://myresults.csv')
The file vos://myresults.csv is now in your vospace forever (until you delete it). Writing out files to vospace of course also works with asynchronous queries.