Maybe just a bit of explanation might help? Of course you can find much info online about PPM. But the general idea of a group of signals are transmitted by sending tiny pulses, where the values of the signals are the time between each pulse. After the last pulse, a long time elapses before the sequence repeats, which the receiver uses to know when to treat the next pulse as the beginning of a new incoming group of signals.
With that in mind, here's some attempt to quickly answer some of your questions (the ones I can understand)
And how long between calling write and the thing actually outputting?
It depends on the timing of when you write relative to the PPM signal. If the 4th pulse just transmitted and you write to 3rd value, the new value you wrote will wait until the next frame. Again, that's fundamentally how PPM works. A set of values are repeated transmitted as tiny pulses, where the time between those pulses reflects their values.
Am I modulating data via the difference in time between pulses on each channel?
Yes, that's how PPM works. The library takes care of doing all the work. You could write the values you want it to transmit and it churns away in the background causing the pulses at the correct moments.
Also if I'm communicating between two Teensy boards, how do I mitigate clock drift between the microcontrollers?
PPM is about time between pulses. The transmitter uses its clock to send the pulses. The receiver measures the time with its clock. If the 2 clocks are mismatched, you'll get a slight error. It end up working pretty like an analog signal.
Several of your questions are confusing. Twice you talked about "binary data". PPM signals are fundamentally about the elapsed time between pulses. They don't actually transmit binary data.
I also don't really understand the very first words you wrote "I'm trying to send
high speed PPM signals". PPM is a relatively slow protocol, and it has a pretty much fixed speed.
Maybe PPM isn't really what you want? Difficult to give advice since I really can't get a read on what you're really trying to accomplish here. If PPM isn't the way, these specific answers probably don't really help, but that's the best I can do without understanding your application.