Originally Posted by HTupolev

No. The big defining difference between a time trial bike and a road bike is posture. When riding along flat ground at high speeds, aerodynamic drag on your body is the vast majority of resistance on the system, and a forward TT posture combined with aerobars allows you to massively cut down on your aerodynamic profile and have a relaxed upper body while doing it. Swapping from a not-very-aero wheel to a super-aero wheel might save you a couple tenths of a mph; swapping from a road posture to a proper TT or Tri posture can save a couple mph.

The trick is, getting the full benefit of aerobars isn't as simple as attaching clip-ons to a road bike. Aerobars allow you to support loads of weight on your upper body at low effort, so you can rotate your fit forward on the bike; seated position farther forward and a bit higher, handlebars lower. Some road bikes can sort of be converted to a decent TT fit, but even then, turning it "back into a road bike" gets more involved than just not using the clip-ons. And some road bikes simply won't have suitable geometry for the conversion in the first place.

But, an aggressively-fit road bike with clipons is solidly advantageous over a pure drop-bar road fit. A much bigger bang-for-your-buck gain than aero wheels, at any rate.