Yes, you can read GPIO6_DR, but you probably want to read GPIO6_PSR instead. PSR stands for "Pin Status Register", which reads the actual signals at the pins.
This register is documented on page 965 in the reference manual.
https://www.pjrc.com/teensy/datasheets.html
Normally you would only write to GPIO6_DR. Reading GPIO6_DR can be used to confirm the output values you previously wrote. But if the pin is configured as input, the corresponding bit in GPIO6_DR has no effect.
If you're used to AVR programming, the pin mux & config might also be a new concept. On AVR, turning on a peripheral takes over control of its pins. But some AVR peripherals like SPI leave the pins sort-of configurable by the GPIO registers. What happens if you turn on 2 peripherals wanting the same pin isn't well defined.
These new chips have a mux that selects which peripheral has control over the pin. GPIO isn't special, it's just another peripheral. Likewise, each pin as a config register which sets several options, like the output speed and drive strength. This stuff is all documented in the manual and it's been discussed many times on this forum. But if you only need to set the pins up at startup, the simplest way is to call pinMode(), which automatically takes care of all these details.