In the past, I believe I've used that combination. I haven't used the prop shield in awhile but I never used the motion sensor, just the sound, flash memory, and neopixel/dotstar voltage level shifters.
As I understand it, the featherwing adapter has a MOSFIT or transistor on the VIN pin. If there is power on the VIN pin (i.e. typically from the USB cable if the solder pad has not been cut), then the featherwing will use that power to charge up the battery. If there is no power on the VIN pin, then the featherwing will route power from the battery to VIN.
I believe you don't have to actually connect the VUSB pin to the featherwing. Sometimes I would cut the solder pad, and install a switch between VUSB and VIN to turn off the Teensy. However, in doing so, it would not charge the battery.
I think I once cut the solder pad, and connected VIN and VUSB on the feather wing. I did not directly connect the VIN pin on the featherwing to the Teensy, but instead put a switch between featherwing VIN and Teensy VIN. This would allow the battery to recharge without power going to the Teensy (i.e. if I had a prop with flashing LEDs and a battery, I could recharge it overnight without removing the battery). I now prefer the Teensy 4.x method of having the Teensy power down if the ON/OFF pin is connected to ground for a period of time.
The prop shield doesn't have a pin for VUSB. I tend to use female stacking headers on the prop shield so it can be mounted above or below the Teensy. On the featherwing, I tend to use long male pins to connect both the Teensy and the featherwing as well as having pins to connect to the breadboard or stacking headers. On the outside pins for the featherwing, I use female headers so I can attach other feather wings.
This way I would put the prop or audio shields underneath the Teensy, connecting it to the breadboard. I would then insert the Teensy on top of it.
In a few Teensy 3.2's, I soldered a PCB that I ordered that fit between the Teensy and featherwing adapter to bring out the 10 pads underneath the Teensy.
Now with the Teensy 4.0, there are some modifications that you have to make if you use the featherwing (connecting 3.3v to AREF in the featherwing, not connecting the on/off pin to the audio output, and not using analog audio output, not connecting the A10/A11 pins since the Teensy 4.0 doesn't have A10/A11 in those positions).