Can the ACRIS Search Pro plugin also be used headless?

Yes. In headless search, the following contents are available under the "extensions" in the Store API response:

acrisSearchConfigs - Configuration "Searchable Content": Specifies which shop content is searched, including the fields to display
acrisSearchTotal - Information about which content was found: Assistance for displaying a search result with a list of all found content including the count
productManufacturerSearchResult - Search results for manufacturers (optional depending on search result and configuration)
categorySearchResult - Search results for categories (optional depending on search result and configuration)
landingPageSearchResult - Search results for landing pages (optional depending on search result and configuration)
... additional results (e.g., acrisFaqSearchResult) - Depending on the configuration of the searchable content