If a bike has aero shaped tubesets it will save the rider watts vs. a round tubed bike
The bike accounts for 15% of drag, rider is 85%.
If a rider position isn't optimized then the drag reduction could be negated partially or even entirely.
Aero tubesets are just better then round
Sadly, in many cases this is not the case.
Girth of the tubesets on the downtube (along with girth of head tube) are key factors in how aero the frameset is.
There are multiple frames that simply test terribly relative to their competition and in some cases provide no advantage (Scott Plasma 1, some older C'dales, some Ceepos, Beyond Fab, Isaac Aerotic) because the headtube and downtubes are frickin' huge and fat relative to their less turbulent competition.
There are also cases of properly shaped tubesets with appropriate girth (or lack of it) set up with forks that create more turbulence than minimize it.
Exotically shaped tubes and hidden brakes are aerodynamic
The front brake mounted behind the fork creates more turbulence then on the headtube.
Many of the really pointy frames w/a gazillion different angles look cool, but it's a marketing feature and many smaller outfits simply don't test the bikes in the wind tunnel.
What to do?
Find a bike (that fits your morphology) that has actually been tested in a wind tunnel as part of the engineering process, not as an after thought to market it.
Generally larger manufacturers (Trek, Giant, Felt, Cervelo, etc.) will have budget to do this, smaller outfits many times have licensed rights to place their name on a frame that is generic (Planet X, Beyond, XLAB and so on).
Net, I'm not really partial to any frame or manufacturer at all.. It's important to be real about what you're going to ride if being "aero" is important to you. Buying a frame that looks cool to you with aero as after thought is not the end of the world but it is willfully ignorant if you're a competitive athlete, e.g. place is important to you.