In the grand scheme of things, you're overclocking a $20 microcontroller board. People overclock their several hundred dollar graphics cards and PC motherboards all the time. Much like PC overclocking, theoretically you're risking the hardware, but actual damage is very rare. Usually the processor just locks up or does wrong things, but usually works fine when you run again at lower speeds.
When you press the button on Teensy 3.1, the Mini54 takes over. It hard resets the MK20 chip. When your finger releases the button, the Mini54 starts it up again at only 24 MHz. This always should recover from overclocking crashes. Well, unless the chip got damaged, which it theoretically possible but very unlikely.
168 MHz is not very stable. Reports are mixed on 144 MHz. Many people say it's working well, but a few have reported crashes after long periods. So far, consensus seems to be 120 MHz works very well.
120 MHz is also a bit special. Even though the CPU isn't as fast as 144 or 168, this speed has the fastest peripheral clock, because that clock must be an integer divide of the CPU clock. If your project is I/O bound, especially with SPI, this speed can let you get 30 MHz SPI clock rates, instead of the usual 24 MHz maximum. Sometimes that matters more than the CPU speed.