An app was previously downloaded on a phone with the same Apple ID as mine but then was later deleted. My question is, since it is already on the cloud, will it still go to other devices with that Apple ID?
Welcome to Ask Different.
Yes, any downloaded app can be run on any other Apple device as long as
- The device is signed-in with the same Apple ID that originally purchased/downloaded it.
- The app supports running on that device.
- The app doesn't have any limitations on the number of devices it can be run (some apps limit the number of users and/or devices).
The software won't automatically be downloaded to the other devices, however. You must download the app specifically.
Your question reads like an XY problem so if you want add the exact issue you're trying to resolve you can  your question.