In general terms, it will increase, but its more complex than that....
Ketchup exhibits thixotropic behaviour, so that at any specific ttemperature the viscosity will vary dpending on the amount of time that a specific shear force has been applied to it.
So if you take a bottle of ketchup and turn it upside down the ketchup will hardly move. But shake the bottle a couple of times, and the ketchup flows a bit faster. Shake it a lot, and the ketchup is much more fluid.
That is because each "shake" applies more shear stress to the sample, causing the viscosity to fall. Once the shear stress is removed (you stop shaking and the bottle is left alone) the structure of the ketchup gradually rebuilds again, as does viscosity.
Ketchup contains both naturally occurring and added sugars, which are dissolved in the continuous phase (water/vinegar). This means that as temperature is lowered, there will be an increase in the viscosity of the continuous phase, and therefore of the measured viscosity of the ketchup when ketchup is cooled.
But at any specific temperature, the viscosity will fall from an initial higher value to a lower value over time. Therefore it is not possible to quote a single viscosity figure for ketchup at a specific temperature. You would need to quote temperature, shear stress (or shear rate - the rate at which the ketchup is forced to move under the stress) and time.
Viscosity of ketchup is often measured using a controlled stress or controlled rate rheometer. In this apparatus, the ketchup is held between a cone and plate and either (controlled stress) a set stress is applied to the cone, and the speed at which it rotates in the ketchup is recorded, or (controlled rate) a specific rate of rotation is applied to the cone and the resistance to rotation is measured. From this, a curve of viscosity vs. time can be generated.