Copying my comments from  issue 870123 :

To accomplish this task, you'll need to make a modification to the dialog class at [1]. Currently, that class only has a static Show() function, but it does not have a way to tell clients whether the dialog is showing. You'll need to add that functionality as well as adding some sort of observer pattern to be notified when the dialog has been closed.

[1] https://cs.chromium.org/chromium/src/chrome/browser/ui/webui/chromeos/multidevice_setup/multidevice_setup_dialog.h

Let's hold off on implementing this until we figure out how we will fix issue 884089. If we end up no longer using WebDialogUI, we would have to change how this fix is implemented.

Ryan had mentioned that he wanted to take this on and had a clear picture of how to do so. Assigning it to him for now once his P1s are closed out.

Issue 892699 has been merged into this issue.

The following revision refers to this bug:
  https://chromium.googlesource.com/chromium/src.git/+/da04be725790ee1d7e2757c29e1a21b80e2472f7

commit da04be725790ee1d7e2757c29e1a21b80e2472f7
Author: Ryan Hansberry <hansberry@chromium.org>
Date: Fri Oct 05 18:44:11 2018

Smart Lock: Delay showing the 'Chromebook added' notification.

Delay showing the 'Chromebook added' notification until the
MultiDeviceSetupDialog has been closed.

R=jhawkins@chromium.org, khorimoto@chromium.org

Bug:  883069 
Change-Id: If8ae079f77de89cede94ea840e5335445fb7a0ad
Reviewed-on: https://chromium-review.googlesource.com/c/1260304
Reviewed-by: James Hawkins <jhawkins@chromium.org>
Reviewed-by: Kyle Horimoto <khorimoto@chromium.org>
Commit-Queue: Ryan Hansberry <hansberry@chromium.org>
Cr-Commit-Position: refs/heads/master@{#597213}
[modify] https://crrev.com/da04be725790ee1d7e2757c29e1a21b80e2472f7/chrome/browser/chromeos/login/easy_unlock/easy_unlock_service_regular.cc
[modify] https://crrev.com/da04be725790ee1d7e2757c29e1a21b80e2472f7/chrome/browser/chromeos/login/easy_unlock/easy_unlock_service_regular.h
[modify] https://crrev.com/da04be725790ee1d7e2757c29e1a21b80e2472f7/chrome/browser/ui/webui/chromeos/multidevice_setup/multidevice_setup_dialog.cc
[modify] https://crrev.com/da04be725790ee1d7e2757c29e1a21b80e2472f7/chrome/browser/ui/webui/chromeos/multidevice_setup/multidevice_setup_dialog.h