I submitted an app using this code to the Mac App Store, and Apple approved it:
Objective-C
WebPreferences* prefs = [webView preferences];
[prefs _setLocalStorageDatabasePath:@"~/Library/Application Support/MyApp"];
[prefs setLocalStorageEnabled:YES];
Swift 3
var prefs: WebPreferences? = webView.preferences
prefs?._setLocalStorageDatabasePath("~/Library/Application Support/MyApp")
prefs?.localStorageEnabled = true
Whether they will continue to approve that, I don’t know, but they allowed it for my application as of 2011-01-29. Update: They also approved a version update to the same app, so it has gone through twice.