In such a scenario, is it possible to use Facebook Messenger app without having an active Facebook account?

Yes, it is.

Open Facebooks deactivateaccount page.2.

How To Use Facebook Messenger Without A Facebook Account

Ignore the photos of the people who will apparently miss you and scroll to the bottom.3.

The last option says you’re free to continue using Facebook Messenger even if you deactivate your account.

ensure this is not checked and just leave it as is.4.

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Scroll down and hit Deactivate.5.

Now, your Facebook account will be deactivated.

All your Facebook data will be safe until you are ready to get in again.

like note that your deactivated Facebook account doesnt get reactivated, if you are using Messenger.

Your friends will only be able to contact you via the chat window in Facebook or the Messenger app.

Download Facebook Messenger on iOS, Android, or Windows Phone.2.

launch the app and put in your phone number.3.

You will get a code via SMS to confirm your number.5.

source: www.techworm.net