Will this wifi adapter work with librem 14?

I do plan on running pureos with boxes vm - kali and parrot os

if not will this work ?

For the first one … it depends on how much hassle / how much compromise / how much risk of fail you are prepared to accept. https://linux-hardware.org/index.php?id=usb:0bda-8813

On the other hand, your link says Linux kernel support. Maybe interrogate the vendor more closely.

Does not work the Monitor Mode or something in the built-in wlan card on Libre 14?

Looks, as requested, very negativ for AWUS036NHA on any Linux distibution. Anyway, archiv link for AWUS036AC_ACH_Linux_v4.3.14/driver/ on Linux (for rtl8821AU) is here: https://www.wlan-shop24.de/treiber-und-firmware-download. Closer look at AWUS036AC and AWUS036ACH files might help choose or not to choose (change current setup) any of those for L14.