Probably not, avr-gcc is gcc for an AVR processor such as used in an Arduino Uno or Mega...
The Teensy 3.x boards are ARM based boards, so require a different compiler. You can build programs for the Teensy using the ARM based compiler, that is installed with Teensyduino. You can also use makefiles to build with this compiler and the like. There are also setups that allow you to use other IDEs and the like, including a Visual Studio setup or using Eclipse,, or ...
Not sure what you mean when you say you wish to practice avr-gcc? If you are saying you wish to practice C or C++ programming than yes you can do this.
If you wish to practice doing stuff specific for AVR processors, than you can do some of this with a Teensy as Paul has done a good job of emulating a lot of the AVR registers and the like, to map them to the ARM setup, but there are differences.
Again sorry I am not sure what you are really asking?