Hi @OliverPickburn,
Once you have set or modified the desirabilities of your responses, you can use the option "Save Desirabilities" in the red triangle next to Augmented Prediction Profiler (or next to any Profiler):
- Original situation with desirabilities :

The run added using the default "Max Expected Improvement" has these factor values:

So to answer completely your question, changing desirabilities will not change the candidate set created to rank the points to test in next iterations, but it will change the ranking and selection of points as it will be linked to acquisition function and desirability functions.
Like for DoEs, the Bayesian Optimization platform do use and take advantage of several metadata/information from the column properties (coding, design role, response limits, etc...) or table script (constraints...).
Hope my answer is clear,
Victor GUILLER
"It is not unusual for a well-designed experiment to analyze itself" (Box, Hunter and Hunter)