I guess it's possible but really I think it's unlikely.
Consider that SpaceX was created for the sole purpose of reaching mars so that Elon Musk could be buried there. Reaching mars is the first step in colonizing it, and if any company would ever do something like that - it would certainly be SpaceX. Along with that, it would be fairly quick since they are working at a rapid pace towards space domination.
However, even if it takes 200 years to reach space - we will just more likely be using Bitcoin as our main currency by that point. USD has been used for close to 200 years now, as well as other world currencies, so I think it's still possible and even likely we would be using Bitcoin.
It may even be a vastly improved version of bitcoin, but since Bitcoin is a software and not a physical item, it can become something entirely different but we can still call it Bitcoin, and it will still be Bitcoin.
#ToTheMars!
There will be digital currency in an planetary financial system. Most of the goods, if not all, would be digital. But, given that we have 3d printers now they could easily be physical. There is still the question as to the speed - for all currencies. Maybe 22 light minutes is not a big problem or by then there is a trick to speed it up.