You are correct; if you don’t have initiative then the entire ability will never trigger and won’t do anything.
The if statement there is an “intervening if clause”, meaning that it not only is a condition to get the effect of the triggered ability, it’s also a condition to have the ability trigger at all.
603.4. A triggered ability may read “When/Whenever/At [trigger event], if [condition], [effect].” When the trigger event occurs, the ability checks whether the stated condition is true. The ability triggers only if it is; otherwise it does nothing. If the ability triggers, it checks the stated condition again as it resolves. If the condition isn’t true at that time, the ability is removed from the stack and does nothing. Note that this mirrors the check for legal targets. This rule is referred to as the “intervening ‘if’ clause” rule.