I have a seatpost only rack too (the Bagman), it's a good one- but no way strong enough for even one modest bag of groceries. Don't forget the weight would get it bouncing as well. Something would surely break (seatpost, saddle rails, rack itself...)
My grocery/errand bike has a good sturdy 'regular' rack. You won't regret getting a sturdy rack made for carrying a goodly weight.