Why not, i've done it since day one.My probe is taped to the side of one bucket with some insulation.
Why are you taping and insulating the probe to the bucket?
The idea would be to get a more accurate reading of the temperature of the wort in the bucket instead of just the air temperature in the fermentation chamber. They can be quite different.
I can understand if it's just a temperature probe to display the temperature, but I would not connect the fridge temperature probe to the bucket or immerse it in liquid.