Track whether a given user session has completed initialization, and use

components/user_manager/fake_user_manager.cc

Index: components/user_manager/fake_user_manager.cc
diff --git a/components/user_manager/fake_user_manager.cc b/components/user_manager/fake_user_manager.cc
index f05eb58709b864bd5feca9a513decaf83323e6cd..fac0724d6de169f52b6e2ce682ed84ce72ab843b 100644
--- a/components/user_manager/fake_user_manager.cc
+++ b/components/user_manager/fake_user_manager.cc
@@ -54,6 +54,10 @@ const user_manager::User* FakeUserManager::AddUserWithAffiliation(
   return user;
 }
 
+void FakeUserManager::OnProfileInitialized(User* user) {
+  user->set_profile_ever_initialized(true);
+}
+
 void FakeUserManager::RemoveUserFromList(const AccountId& account_id) {
   const user_manager::UserList::iterator it =
       std::find_if(users_.begin(), users_.end(),