Could I index both products and the sites “normal” text pages so users can search both in the same search field?
Depending on your integration, absolutely. Since an Algolia index is schema-less, you could commingle the two type of records in a single index with different fields, or you could build two separate indices and combine them using a federated search interface like this:
How you get the records into your index depends on your integration – if you are using a direct integration with your e-commerce platform, you may need some additional code or the Algolia Crawler to ingest the additional pages. Otherwise you can ingest the text in your website build process.