There are really two questions here: Can I add an extra TField, and can I add an extra data field.
When you clone a client dataset cursor, you end up with two TDataSet instances, each with their own collection of TFields, which share a single data store. You can certainly add additional TFields for things like calculated fields to one or the other without affecting the clone. There is no problem with doing this.
But remember, the original dataset and its clone share a single data store. You cannot change that data store without affecting the other dataset. If you add a new field to the data store, then that new data will be present in the store referenced by the original dataset, whether or not you have created any TField objects to read/write it. If this is starting to sound like a bad idea, well, that's what I'm thinking, too.
Finally, if you want the original dataset and its "clone" to have different data stores, then you can assign the Data property instead of using CloneCursor. When you do this, the data from the original is copied into the data store for the "clone", but the original and "clone" no longer share a single data store.