Yes you certainly can overcharge a cars battery with a battery charger and I've done it myself when I forgot to unplug the battery charger one night due to being over tired and I ruined the battery since overcharging the battery boils out the acid and kills the battery.
A battery should get fully charged with a battery charger within a few hours so check on the battery every few hours to see how much charge it has in it and if you need to charge a battery overnight put it on the trickle charger which will charge the battery up more slowly to prevent overcharging the battery.