Yes, Its work ,Go to your FB profile, click the About tab, then under "Contact and Basic Info," look at the section under Contact Information > Mobile Phones where your current numbers are listed.
- Mouse over one of your existing numbers and a little pencil icon and the word Edit will appear to the right. Click "Edit," then click "Add another phone."
- Select US for the country, enter your GV number, set who can view the number, then click Save Changes. The number will save!
- Now go to your Mobile Settings (https://www.facebook.com/settings?tab=mobile) and you'll see your GV number listed under "Your phones." (From here on out, I'm not sure on the exact wording because I'm going from memory.)
- Your GV number will be shown as unverified. Click Verify and it shows a dialog saying something to the effect of "We can't send you a confirmation code because you've opted out of receiving texts from facebook. text the letter "f" to 32665 to opt back in and get your code. Paste it into this dialog once you get it."
- Go to GV/Hangouts and text the letter "f" (without quotes) to 32665.
- In a few seconds, you will get a reply back from Facebook with the confirmation code. Paste that into the dialog on Facebook and your number will be confirmed