People regularly use Thuja as bonsai so the container isn't really the issue. The problem is how you care for your tree.
I suggest not putting 2 plants in the one box. It is going to cause you headaches in a couple of years time. The problem with growing in containers is space. This problem is going to be compounded having two plants squeezed in together. Root space, available nutrients and water would be a much larger problem with two plants.
To begin with you are going to want a good quality soil. If you have a good quality soil you can get away with only having to replace the soil every two years. Even if you feed the plants with slow release fertilizer I would still suggest pulling the plant up, trimming the roots and replacing the soil.
The size of the box as well as available nutrition (food/water/sunlight) will determine how tall your plant grows. If you trim the tree and trim the roots every couple of year you can keep it in the same sized container forever.
With potted plants your challenges to keeping a healthy plant are:
- Adequate sunlight
- Appropraite watering
- Healthy soil
- Healthy root growth (not root bound)