So... after creating a video for this answer, it's clear that the default view hides disabled products using some form of Drupal magic. But I will still go through how to make the status get indexed so you can filter it on Views. Maybe you need this for a non-magical Views implementation?
STEP BY STEP
1) Go here admin/config/search/search_api/index/product_display/fields and check "field_product:status"
2) Go here admin/config/search/search_api/index/product_display/status and re-index
3) Go here admin/config/development/performance and Clear Cache
4) Go here admin/structure/views/view/display_products/edit and a filter for "Product variations: Status (indexed)"