dont want to speak for him... but seems to me there's no way to predict this without seeing schemos of the equipment in question...
possible issues because of differing grounds...
possibly the impedence of one is appreciably lower and the phantom from the other is sucked down till burning the build out resistors in the phantom circuit or the phantom could fail entirely...
bottom line dont use Ycords...
Yes, it would be somewhat unpredictable. But I think we have to assume, to start with, that gear is not absolute poorly-designed garbage (if it is, why record with it?). For example, 48V/6800 ohms = 7mA * 48V = 0.34W. That's grounding out the phantom supply, worst case scenario. So in theory, a phantom supply resistor should be 1/2W rated. But it probably won't die a horrible death even if it's 1/4W; the phantom standard is supposed to be 10mA per input, which is 5mA per resistor, or 0.24W.
So I don't worry too much about the phantom resistors. Resistors are fairly durable. Opamps often are not. But again, you'd have to presume that the gear was not garbage, so you hope there is some overvoltage protection at the gear's input. Otherwise, the mere act of switching phantom on or hotpatching a cable could destroy the opamp. Some opamps have internal protection, but diodes are very very cheap, so why not use them? And most schemos I've seen do.
Anyway. So put caps in series with the split to the recorder (where phantom is presumably coming from the live board). That may be unnecessary, as that box most probably has its own input caps.
Even without that, you probably don't want to turn on both phantom supplies. Most likely that would just cause a drop in the phantom supply impedance, which for most microphones would not matter at all. But it still seems funny, doesn't it?
If you have a problem with the ground reference between the two bits of gear, that is a potential problem irrespective of phantom power. If you want a Y cable to work, you ought to be sure the bits have a low-impedance connection to a common ground. The phantom voltage reference (pin 1) ought to be chassis ground, although in many boxes that may not be true.
If there is a difference in signal ground, you'll have the same problem with using an unbalanced insert send . . .