Birkat HaMazon immediately after hearing the zimun

Shalom, I would like to know whether the common practice is acceptable: after one person makes the zimun and recites the first blessing of Birkat HaMazon aloud, some of the diners do not recite it together with him, and afterwards they go to wash mayim acharonim and each one recites Birkat HaMazon individually, without eating anything after the zimun. I would also appreciate specific sources. Thank you in advance.

Shalom u-vracha 

It is permissible to do so. 

See Shulchan Aruch, Orach Chaim, siman 200. 

And siman 194, se’if 2. 

Have an additional question on this topic or need clarification? Leave your comment below. (Please note that the comment will not be published but will be sent directly to the answering Rabbi for review and a private response)