It should be possible to connect the PCA9685 to a PICAXE.
I2c is fairly universal and the PCA9685 supports Standard (100 kHz), Fast (409 kHz) and FastPlus (1 MHz) clock speeds.
Been using Adafruit PCA9685 & Picaxe on my yak for lighting effects for a couple of years, works great. The frequency is adjustable 40Hz...1000Hz so works great for servos & LED lighting (via MOSFETs) (defaults to 200Hz which works fine on either). Each of 16 channels may have a different PWM value (set it & forget it).
Need to use a separate +5v supply for driving lots of servos.
However, found it best to use PWM off Picaxe-20M2 for motor control.