If the triggered ability does trigger, that ability will check Ayara's Oathsworn again as it tries to resolve. If Ayara's Oathsworn has four or more +1/+1 counters on it at that time, the ability won't resolve. None of its effects will happen. You won't put a +1/+1 counter on Ayara's Oathsworn and you won't search for a card.