[ProfilePicker]: Do not show the picker if Chrome has only one profile

The account picker isn't supposed to be shown to single-profile users.

This change would also make it easier to write browser tests that
enable the features::kNewProfilePicker flag, since they will land
directly in the browser.

Bug: 1063856
Change-Id: Id947d21686503bb068d4ce7b83c2f88889b064ab
Reviewed-on: https://chromium-review.googlesource.com/c/chromium/src/+/2324847Reviewed-by: David Roger <droger@chromium.org>
Reviewed-by: Monica Basta <msalama@chromium.org>
Commit-Queue: Alex Ilin <alexilin@chromium.org>
Cr-Commit-Position: refs/heads/master@{#792738}

chrome/browser/ui/startup/startup_browser_creator.cc

@@ -269,7 +269,10 @@ bool CanOpenProfileOnStartup(Profile* profile) {
 
 #if !defined(OS_CHROMEOS)
 bool ShouldShowProfilePicker() {
-  return !signin_util::IsForceSigninEnabled() &&
+  size_t number_of_profiles = g_browser_process->profile_manager()
+                                  ->GetProfileAttributesStorage()
+                                  .GetNumberOfProfiles();
+  return !signin_util::IsForceSigninEnabled() && number_of_profiles != 1 &&
          base::FeatureList::IsEnabled(features::kNewProfilePicker);
 }
 #endif  // !defined(OS_CHROMEOS)