Post testing /pep failure question

So, I just want to get clarification if anyone knows but if you have hiv symptoms like a fever, headache, fatigue etc. and you get a 3rd gen antibody test . That test should be able to pick up if the current symptoms are hiv or not? Since if they were caused by hiv then it would mean antibodies are present mounting an immune response and so detectable?

Or is my logic flawed??