My outdoor cat's leg wound drained pus. Can it heal without stitches?

It sounds like he had an abscess from an injury, probably an altercation with another cat. A veterinarian would likely not suture it anyway to avoid trapping any contaminants and causing another abscess. It looks pretty clean with healthy granulation tissue forming. The antibiotics, even intermittent have probably helped keep further infection at bay. Keep an eye on it, if he will let you, clean it gently with a damp clean washcloth and keep any debris or infected material cleaned out. It should heal from the outside of the wound to the inside, gradually shrinking and closing over the open area. As long as he continues to eat and drink and behave normally, and and the wound continues to look clean with pink and healthy tissue, he should do fine. He needs to eat, going without eating for more than a few days will cause liver problems in cats which would require a vet visit to be treated.