Is this just a no no. I mean I like a cycling cap but with the peak raiser would this just counter any aero gains made by the helmet ?
Having no scientific backing or CDA anyaysis to draw upon, on the surface it appears that no cap would be the way to go.
And does the ‘kool’ factor …peak up/down…also become a problem 
My guess (bro science) if you’re doing TT then no cap… If anything it doesn’t make that much different cus your head area is already blocking the wind. Kind of like the big sunglasses doesn’t change actual shape of your head so no watt loss there.
What if you really need a haircut and your hair is sticking out the vents of your aero road helmet? 
The Youtube videos posted by Specialized on tests conducted in their Win Tunnel are excellent and should give you a good idea of the power/time savings of everything related to cycling (e.g. frame design, body position, clothing, shaved legs, etc.).
https://www.youtube.com/results?search_query=specialized+win+tunnel
For example, in the video on aero helmets they show that a rider would save 60 seconds and 40 seconds, respectively, by using their TT helmet and their RR Racing helmet (Evade) over their well ventilated road helmet, the Prevail (used by Peter Sagan even during sprint finishes in the tour).
Regarding a cap, if you watch enough videos you will easily understand that air disruption would be significant and therefore not something a racer would do. However, rough guess based on other #s they publish on other items is that a cap’s flap would cost you 1 to 2 minutes (dependent on whether flap up or flap down) over a 40K TT (hour at 25mph).