You can't use Arduino with Teensy without Paul Stoffregen's bootloader chip so this won't be Arduino compatible.
A few years ago I did a bit of work with Teensy & ESP8266. I made a development board (primarily for students) using Teensy 3.1 & ESP01.
To program the ESP I used a 'pass through' loaded on the Teensy in a 'serial in -> serial out' arrangement
I used it a lot but began to realise that ESP8266 did almost everything I wanted anyway.
Ian