What happens if the relative soil moisture in bucket 2 is higher than 100%? Does it affect the water balance in bucket 1?

No, it does not affect bucket 1.

The only flow component affected by the full saturation of bucket 2 then is base flow which would be larger than the deep conductivity. But does this have physical explanation? I mean, should I try to avoid this situation in my model?

Yes, the base flow is the only flow component that will be affected. Although it will be larger than the deep conductivity, the physical justification is that it approximates the increased interflow that would have occurred if the water had not flowed from bucket 1 to bucket 2. However, it might be best to avoid this situation in your model.