Can hybrid bikes be as fast as cyclocross bikes if we use an aero position instead? Can hybrid bikes be as fast as cyclocross bikes if we use an aero position instead?

There's quite a lot in common for both bikes. People claim that CX bikes are faster. It seems like the main reason is because they're more aerodynamic from the rider's posture. To have a more aerodynamic position on the hybrid bike, my guess is that the stem needs to be longer and have a lower angle.

Advantages of using a hybrid bike include not having to buy another bike if you already have the bike, lower cost for a bike with similar features such as brakes and drivetrain, better leverage for braking compared to that of the hoods position, more room for accessories on the handlebar compared to that of a drop handlebar, possibly more room for a front basket, more options for mirrors, less expensive combo shifters, etc.

On my hybrid bike, When I rotated my hips forward, I found it easier to pedal smoothly just like on my road bike. It looked more like the posture used for road bikes. When I was more upright, I found it harder to pedal smoothly and had to remind myself to do it more often. My heart rate seemed to be higher and I felt slower. Maybe smoothness of pedalling allows more power to be produced at a given heart rate.

On my road bike, my preferred position is on the hoods. I rarely use the tops or drops position. I find the drops position awkward. It's possible because my bike is one size too large. I'm 5'7" and my bike's 56 cm. Also, my commute is almost 9 km.

If a hybrid bike was fitted so that the posture was similar, wouldn't it be almost as aerodynamic?
Is that not a popular alternative because with an aerodynamic position, our core and arms can get tired or stiff, and we don't have alternative positions available?
For a properly fitted hybrid bike, is it supposed to be harder to pedal smoothly compared to using a properly fitted CX or road bike?

Update:
I got my hybrid bike performance fitted. The fitter mentioned that the geometry was like a cyclocross'. My posture's more like a road bike's and was optimized for both aerodynamics and power transfer. Since there was a basket, it could only go so low. It's good to be able to have proper form. The next time I commute, I'll see whether I'm faster. A benefit of a longer stem is that there's more room for accessories.

Here are the details:
SH: 737mm
OS: 30mm
Reach 545mm
Drop: 75mm
Handlebar: 45mm riser bar, 600mm wide
Stem: 130mm +/-10°
You're right to say that aerodynamics plays a big part. I'll assume the same tyres and saddle, and rigid forks. 

The geometry of a hybrid may not lend itself to efficient pedalling if you increase the reach and decrease the stack, and handling may suffer from the longer stem.

The important part of the drag is CdA, the product of the drag coefficient and the cross-sectional area. The biggest effects come from reducing the area by getting lower as you suspect, but also by getting narrower, and there's a big difference there. I cut my hybrid's bars down from 640mm to 590mm and tilted them slightly forwards so the slight rise in the bars contributes as much to length as to height. My tourer (not a bad model for a cyclocross bike) has something like 450mm bars. The different hand positions also mean that any bend in your elbows tends to make you wider on flat bars.

To give you some idea of the difference, a 67km ride I've done quite a few times comes in at 3 hours on the hybrid but I've beaten 2.5 hours on the tourer, before I was really in training. Tyres were similar but not identical, and the load was no worse on the hybrid (backpack; I usually use a pannier).