Dependent variable is more like label (but high cardinality)

I have a very fundamental question about dependent variable, which is not like ‘price’ but more like a label but having very high cardinality. It’s like some ID of a row or ‘product_id’ in true sense. This product_id can range from 1-100K.

  1. Can we have ‘Y’ as label/ID with such large value for prediction? We can surly use log function but the back conversion to absolute value may not produce exact ID.
  2. Do we need to have that large FC layer for this to get resolved?

Any hint would be beneficially. Thanks!