With the current DR setup, no, you wouldn’t see the secondary start up automatically. There is a manual command (invokable through the fdbdr command line utility) that can switch the primary and secondary in a running DR pair without any data loss as well as stop a DR so that the secondary is unlocked (in the case of, say, a meteor strike hitting a data center).
The general advice is that clients should live inside the DC (or near the DC) where the cluster is located, so something like running two sets of clients, one each DC, where each client only has a cluster file that connects to its side might be reasonable. (You can also detect whether a cluster is up by seeing if you get the “database_locked” error back from trying to read from it.) If you’re in a situation where this is easy, you could also conceivably only spin up the secondary side once you’ve noted that you need to fail over.
Alternatively, you could provide clients with both cluster files and then create one Database object per cluster. Again, you could conceivably notice which ones are hot by seeing which ones return “database_locked” when reading. There is also a system key that (if ye be brave or fool enough) you could read to see if a cluster is locked if that’s more your speed.
In the new DR configuration currently being developed on the master branch, there is only really one cluster with one cluster file, and any operations from the “cold” DC will be slower, but they should still be possible. The system will usually be configured to automatically fail over, and if you do nothing, then everything should continue to work with degraded performance. It would be better if, in the case of a failure, you also switch to using app servers closer to the hot side, but that’s not strictly required. A split brain is avoided by (1) electing a master in a DC (based on priority) that can talk to a quorum of coordinators and (2) recruiting the other components of the transaction subsystem in that same region. The quorum requirement on coordinators stops more than one master being elected.