Suppose I have a DC/DC converter that's rated for 2250VDC isolation for one minute. If I put two of these devices in series, making sure to maintain proper clearances on my PCB, do I get an effective isolation voltage of 4500VDC for one minute? Am I still limited to 2250VDC? Do I get something quantifiable in between?
If the insulation on one fails, the remaining one will cop 4,500 VDC which will definitely make it fail.
There's also no guarantee the voltage will spread evenly across them - the insulation on the devices might be measured in MΩ, but if one device is 1 MΩ and the other is 3 MΩ the voltages across each will be 1,125V and 3,375V and you are in for a bad day.
It also bears mentioning that the 2,250 VDC one minute rating is a withstand rating, not an operating rating. You should not plan to apply this voltage to your device except to withstand the consequences of a malfunction.
Applying 2,000V on a regular basis is likely to cause cumulative damage. For example, "Megger" (hi-pot) testing a 440V cable using a 2,000 VDC test source is considered a good way to find cable insulation faults because it will blow through weak insulation and make minor faults into severe faults (which are easier to detect.)
In general yes. assuming your two systems have same impedance, then the voltage drop across each will be 1/2 for same series current. this is ohms law.
More specifically, there is a lot more to consider, the least of which is if your system will still operate properly if it is floating (only one of the two systems will be referenced to ground!).