Running engine without heater hoses attached
 

I'm doing engine running in without the heater hoses to the flapper boxes attached to the heat exchangers

Can it do any harm? would it negatively affect de mfi thermostat? I know the thermostat respons to the heat provided, but maybe the hot air is not delivered in sufficient quantities.

Any drawbacks that people know about?

The MFI thermostat needs a forced hot air supply to function.
The MFI race cars use a cockpit hand lever to manually move the rack in/out in lieu of the forced air. Your car will run very poorly (rich) without an operable thermostat. Not the best conditions to be breaking an engine in.
Bill K

OK, but would there be a relevant air pressure difference if the hoses are off vs connected + flapper boxes set to just dump into open air?

yes

Additionally, having the heater hoses attached helps evacuate the hot air that sets in the heat exchangers, allowing the engine to run cooler. If you run the engine this way for a prolonged amount of time, it will be like running it with the old thermal reactors.