As Algolia's Query Suggestions are not linked to a specific product but rather to a popular search term, the out-of-the-box functionality would not include images. Query Suggestions are different from search results. Query Suggestions are only suggestions of better queries.
Because the Query Suggestions index is populated by analytics data, there would not currently be a way to upload images as part of the frequently-updated suggestions data (as shown in our documentation on the Query Suggestions index schema) based on the most popular searches.
However, you can create a separate index for the most popular searches and include specific images that you would like to showcase for each suggestion. Please note that in this case you won't be using our Query Suggestion builder and you would have to rely on your external data only to create such index.