Query Suggestions come from a Query Suggestions index and requests to a suggestions index are counted in the same way as they would be to a regular Index. More on this in our Knowledge Base Article How Does Algolia Count Records and Operations.
What this means is that the number of requests does not necessarily need to increase. For example in this CodeSandBox if you look in the network tab you will see only one request to Algolia per keystroke, but both query suggestions and hits are returned. This is a built in functionality of the AutoComplete library that behaves similarly to multipleQueries. Two index's are queried in a single request, so you get the results from both but are only charged for the single request.
However in the example here in our guide on Integrate AutoComplete with React InstantSearch Hooks the autoComplete menu is returning query suggestions and the instantSearch instance is returning hits but in this case they are using separate requests. This is simply because each library must make its own request, but you can mitigate the number of additional requests by debouncing search results.
This tells the InstantSearch state to wait a period of time before making its request to return the hits. This gives your users time to select the best query from the AutoComplete searchBar before making the additional request for hits.
To summarize, query suggestions do not need to increase the number of billable requests, you have control over the when and how those requests are made.