Yep we spar, many different forms -
1. tegumi, standup wrestling practise, compromised and then non compromised.
2. randori, no pads, controlled contact/pace sparring.
3. bogu kumite, heavy contact, full head gear, light body armour and groin cup. developing this right now.
We of course also have many drills including grab release, hold release, evasion, bunkai practise (develops into 'free' attacks), 2 on one randori etc etc
I have absolutly no concept of how non contact karate can be of much use for any form of application.