Can a teensy 3.2 deliver enough power to properly activate multiple servos by chance?
No. You should provide your own regulator or supply for the servos specified voltage.
This might be an original design, or an off-the-shelf "battery eliminator" intended for an R/C vehicle of similar needs.
Note that the teensy regulator's maximum input voltage is fairly low, and may be in the range of what more powerful servos expect, ie, you might be able to run the teensy regulator off of the servo supply.
Be sure to consider the possibility of brownouts - multiple active or stalled servos can consume a lot of power, and if your upstream supply is not "stiff" enough this can result in the voltage dropping low enough that control electronics misoperate or reset - granted that is less likely with the teensy than with a 5v MCU using a regulator with a higher voltage dropout.