Probably not. What it seems like to me is that it's more for situations like "help >> about" dialogues that currently create an entirely new window just to show some information about the application that already uses a window. With popovers, it probably creates a box without window decorations inside of the current window that goes away if you click outside of it.
I believe you get that through an existent extension which allows dialogs to be joined to the calling window (that's in mutter at least).
Which is why it was moved to (core) Gtk, to not have to learn to check/use/install the extension everywhere else where Gtk works (mac/bsd/windows, kde/etc), because it's much easier to create your own popover than learning to manage that extension on other platforms/environments.
Yes, but popovers are better than info/warning dialogs...
Except if they work like they do in OSX, where you can't move/resize the popover out of the way to check the contents of the window before making a decision. In the case where the popover presents options and to make a decision you have to remember what was being displayed in the main window.
But, I think these popovers are not like that, and actually look like something well designed and useful. It's for things that would not be done with a info/warning dialog at all, but more like a tooltip on mouse over: http://blogs.gnome.org/mclasen/2014/...-now-popovers/