You may have front end widgets that you don't want populated under certain circumstances.
You can't directly control the UI with a query parameter, but you can control whether the facet values are returned.
For example, you can create a rule that prevents a facet from being returned when a specific rule context is sent to Algolia. This will prevent the widgets from being populated with that data.
If you are sending a rule context:
You can then create a rule by selecting the Manual Editor section:
You could detect a specific context and return specific facets based on this context:
In this case, the returned data looks like this:
If you have specific widgets that are expecting data to populate them, you can write conditions that render data based on the facet data returned.
You can learn more about rules and contexts here.
Note that you may also need to edit your panel widget (which is generally the parent of individual widgets -- more information here) to detect whether or not there are facet values in the returned data.
Information on how to edit the template and detect the result from Algolia is available here. You can inspect the options.results object for a better understanding of what is available in the returned data.