Good morning

Yes, the cycle will crash if the beneficial bacteria doesn't have a food source (fish food and waste). I don't know for sure how long the cycle will last once the food source has been removed, in your case the fish. Adding flake food might help to keep the bacteria alive, it just depends on how long it takes the food to decay. It may not decay fast enough to feed the bacteria.
You can always place all the media into a cycled tank that does have fish in it to keep the good bacteria alive. That way should you need a quarantine tank in an emergency you have additional filter media ready to go into the filter for the quarantine tank. Or should you decide on a new tank...then this filter media will be ready for that as well.
Ken.