I think even if they did, the bitcoin users wouldn't use their service because they can do it by themselves. That's one of the advantages of bitcoin. You can transfer money to another person from a different country all by yourself. You don't need to use and pay any service at all except for the small transaction fee. It would just be a waste of funds if they started using bitcoins but they can always implement it whenever they want.
On the contrary, bitcoiners would be using them when for instance someone wants to remit his coins for dollars or any other form of money, so opting to do business with Bitcoin won't put them out of business, but playing the Ostrich would.
These business people can change their course whenever they want. I think that would happen only when bitcoin's starting to take over. But the world wouldn't be needing their service at that point as told in the OP.
Then they would have lost their market share to those companies that saw the vision of Bitcoin and the easiest thing in life is not to unwittingly hand in your rightful position only to start fighting for it again from the bottom! They say, make hay, while the sun shines!!