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