This is an old thread, but someone pointed it to me today... and it looks like I never answered this last question.
Assuming the CPU and memory are actually working reliably at those speeds, the timing functions like millis(), micros(), elapsedMillis, elapsedMicros and IntervalTimer should all be perfectly fine. The code implementing those functions automatically adapts to the CPU speed setting, so you get the correct times even as the chip runs faster.
One place where problems can occur is digitalWriteFast(). By default, pinMode() configures the pins with a feature called "slew rate limiting". This slows the rate of voltage change, only by nanoseconds. The limited slew rate makes a huge reduction in electrical noise and interference, especially if you use ordinary wires without shielding. Normally you want the slew rate limit feature. But at very high clock speeds, digitalWriteFast() becomes so fast that the pin's voltage can't fully change before the next instruction. This was a problem years ago with the ShiftPWM library, which was fixed by adding short delays.
The other known overclocking problem is I2S on Teensy 3.6. Beyond 192 MHz, the I2S MCLK clock generator doesn't work reliably.