Yes, definitely, it might happen, but the government has to accept or adopt it first. When you take a look at some other countries, their government sees Bitcoin as a way of scamming their citizens, which it is not; it's just because the government has no interference or has no concern about your transactions. Your transactions are moving smoothly without any government authority, so in the nearest future they will come to realise the fact that the adoption will surprise them; however, I guess without government authority I don't think banks can make use of it as a medium of exchange.