AnFI - hardly - opposite direction rotors and aircraft without swashplates will be different. Additionally, since phase lag is compensated for by different arrangements of jack position and advance angle (how far the pitch change arm is ahead of the feathering axis of the blades) on different helicopters, the exact tilt of the swashplate will depend on those factors.
John -you are describing an acceleration cross couple that is very evident on the Lynx - a hard pull up needs left cyclic to oppose a marked tendency to roll right. Similarly on other aircraft (Wessex, Sea King) a hard right turn (steep turn or quickstop for example) needs left cyclic to prevent further right roll as the cyclic is brought aft to increase the G.