Can you run a 4 barrel with a 2 barrel cam and heads?

Yes, but why?

Why not run a 2BBL on a 350 HO motor?

We have been over this time and time again. A majority censused first reply why? and the second is for what reason.

Build the motor the correct way and save headaches. Some people here have many years behind their belt and some do not. One who asks the 2/4 barrel question usually has little knowledge on the matter, thus, I always ask why. I would never ask a person who has never built a motor to build me a motor.

I look at the big picture here on the 2/4 swap. Most people are thinking that if they do the swap, their car will be helluva lot faster...this is the mentality. When they get piss poor results, they ask "why"? That is why I say NO on the swap...most people assume result X and only get C. There is way more to this question than a "simple" or "compatible" swap. It is the human perception of the unknown result. I know the general end result of the motor in most cases and know from over 20 years of hearing people doing the swap and their attitude and displeasure with the result.

Do what you want, you will anyhow. I say it is a waste of time and money. Wheras, for $500-700 more (proper cam and heads) you can do this correct.