What will happen if I delete some automatically generated indices (*_suggestions, *_sort)

It depends on your set up. If you are referring to these indices anywhere, removing them will break your instance. If they are automatically generated by your integration, you must ensure you prevent them from being regenerated. Algolia does not automatically generate any indices except query suggestion indices, which you must set up to generate. 

For Magento:

I recommend reviewing this guide on the issue of sort indices and this guide on the issue of editing your suggestions configurations. 

If you delete any indices, you must first ensure:

A) That you are not using them on the front end (which you can address using the above guides)
B) That they are not regenerated after you delete them (which again, you can address using the above guides). 

If you have made any customizations in addition to this you may need to make changes to your front end as well.