I can't tell you specifically for the geared Trail-a-Bike, but we had a non-geared Trail-a-Bike followed by a geared Burley Piccolo (alas out of production). We do ride about 1500-2000 km per year with the trailercycle, which is much more than most people do... Which is why we worn out the articulation of the Trail-a-Bike in about one year.
In some ways, gearing is a gimmick, especially with a 4-6 year old kid. My older one started using the Piccolo at 5, started to shift at 6 and was really into shifting and using the ideal gears at 7. Her idea was to spin at the same speed as I did and was useful both for stoking on the real tandem and for riding her own bike. And I would add that I appreciate her contribution when we climb hills with the loaded bike.
On the other hand, my younger one is about to turn 7 and basically shifts – sometimes – when I ask her. So each child gets it differently.
I also found another issue with the non-geared trailercycle: the gear is way too high. Children have short legs and therefore can spin faster. Yet with the basic gearing, she could spin at 90 rpm on the Trail-a-Bike... when we reached 30 or 40 km/h. Yet it's not when going downhill that I need all the help I can get, it's when I climb a hill or when we struggle at 10-15 km/h with a headwind! So unless you are a fast rider, I would recommend changing the default cog with one that would be anout 2 teeth larger.