Interesting question but I would say no as the book says your aircraft needs to be RVSM approved to enter RVSM airspace and you would need to do this at least twice. Only State aircraft are exempted and ATC need to provide 2000ft separation at all times with other traffic when one is around .a real pain .
That said if you can , do it fast because the (ICAO) plan is to extend RVSM above FL410 very soon.