To reduce the load/cost of algolia, I want to load category and new item pages from our database, and first if the user begin searching using the refinements, are the algolia search activated. to replace the content of the product list.
This seems like a lot of additional code for a small reduction in queries. Unlike search-as-you-type, a category page should only require a single query and (if your index is configured properly) and should be faster than running the query against your database, not to mention the opportunity to improve relevance.
I think the experience of pulling one set of results from the db, then swapping to an entirely different set of results, potentially in a different order, when the search starts would be jarring for your end users.
Are you seeing significant traffic to your category pages without search interaction?