Slack in a chain or belt won't affect cam timing as timing is dependent on the number of teeth in either the chain or belt, not the relative length or tautness. The relation between the cam and crank remains 2 revolutions of the crank to every 1 of the cams. However in extreme cases of say a tensioner completely failing it will cause the motor to run like crap purely because the crank accelerates and then there is a delay on when the cams turn because that slack must be taken up. Often the motor won't run at all.
If there is a bad tensioner in your car, it probably isn't affecting how the car runs, at least at this time. Hydraulic tensioners can tend to make knocking sounds if they are failing.