Good idea BUT - A Very BIG BUT...

Lets Say Mr A makes a post and Mr B, Mr C & Mr D comments on your post, then those comments SHOULD NOT work like messenger like you explain in your post. Because if a 1000 people comment you;re phone will go crazy. 

If ANY MEMBER Reply on a persons comment or (2nd Phase interaction) YES, Then messenger like actions would be nice. Hope you catch my drift here.

:-)