Is it mandatory to have a reset in BT_REG_ON during BT firmware download stage in IF573?

Yes, it's mandatory to do this. 

While you design IF573 PCB module, need to have a GPIO to control BT_REG_ON; with M.2 module, wire to W_DISABLE2. During BT firmware download, need to have reset signal to indicate the firmware loading event.

Here is an example of the script to download BT firmware.

#!/bin/sh
# de-assert BT_REG_ON (assert W_DISABLE2# on M.2 interface)
gpioset 5 7=0
sleep 0.1

# Start firmware download in background

brcm_patchram_plus --no2bytes --autobaud_mode --baudrate 921600 \
                   --use_baudrate_for_download --enable_hci \
                   --patchram /lib/firmware/cypress/CYW55560A1.hcd /dev/ttymxc0 &

# assert BT_REG_ON (de-assert W_DISABLE2# on M.2 interface)
sleep 0.1
gpioset 5 7=1