Yes, I've co-located in the facilities of the respective exchanges... There are many reasons for this, with latency being the primary driver. But access, comms lines, cost and other factors come into play.
As far as DR, that has never come into play. I've never thought about it from a trading strategy perspective. Why? Well, there will be some internal redundancies from the exchange/matching engine/feeds... If the primary site goes, trading more or less halts. These are not necessarily 24/7 critical computing environments. Maintaining stability during the market day is what's important.
In reality, I've had systems go down in a colo and definitely experienced line failures that have taken us out of the market. It is what it is. Your trading strategy needs to incorporate that risk and have the safeguards to handle those scenarios (and a panic button).
As for even gaining access to an exchange's DR site, it may not even be possible.
More details will help us help you, though. What are the players/organizations involved here?