No they are very specific in what they attack, you can have a phage for killing E Coli but it will only kill a very precise subspecies of E Coli. They are so specialised there are many millions, maybe even billions of them and they ignore anything that isn't their target.

This what makes them amazing and awful at the same time. It could take a while to identify the right phage for a bacteria that is killing a patient and you have to wait and see if it works. On the other hand when you find the right thing you can destroy the bacteria without hurting the patient and without destroying other bacteria in the process. Unlike antibiotics you are not going to destroy you microbiome with the right phage.