You can add more embedded data fields to a survey in progress, yes. The dataset will update to include those fields once you publish the revision, but it will only fill the field for data moving forward. You would need to go back and manually fill in the added embedded data fields for your past data before the revision.

Alternatively, if it is a simple calculation you want to add, you can go to your Data & Analysis tab for the survey and choose Create New Field, in which Formula is an option. Here is a support site that describes the math operations you can do, rather simple calculations: https://www.qualtrics.com/support/survey-platform/data-and-analysis-module/data/add-new-fields/formula-variable-creation/

Hope this helps! :)

I can imagine that this might not be an uncommon use case. You can't add the new data as new source using an ID as a key field then? eg when the survey was run recipients wouldn't know if their application had succeeded. We want to go backwards and add the outcome and see if there is any correlation with their initial views. So it needs to be new data added to existing responses.

Last I spoke with Support about this, they had let me know that unfortunately there was no way for the field to back-calculate if it was added as an embedded data field in the survey flow. If you add it as a formula in the Data tab, then it could calculate, but that would be restricted to simple math operations like +, -, power, etc.