Battery charging question?

When I went to turn my car on it was making iffy beeping noises...so I figure battery very weak...can't even try to turn the engine over...it's very cold by the way so I plugged in block heater which may or may not be working. finally I plugged in batter charger. It is 10/2a charger I have it trickling on 2. When I leave it charging and hop in everything sounds hunky dory. I unplug it and it doesn't. The question is: can I try to start my car with it attached?